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BEGIN:VEVENT
SUMMARY:Title TBC
DTSTART;VALUE=DATE-TIME:20230213T140000Z
DTEND;VALUE=DATE-TIME:20230213T150000Z
UID:https://talks.ox.ac.uk/talks/id/7657ff52-baa2-4edb-ab0e-32c51ef20b7e/
DESCRIPTION:\nSpeakers:\nSimone Floreani (University of Oxford)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7657ff52-baa2-4edb-ab0e-32c51ef20b7e/
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SUMMARY:Title TBC
DTSTART;VALUE=DATE-TIME:20230123T140000Z
DTEND;VALUE=DATE-TIME:20230123T150000Z
UID:https://talks.ox.ac.uk/talks/id/7b1dd95f-4f16-4cbf-93d6-aad7952bbbef/
DESCRIPTION:\nSpeakers:\nMichael Drmota (TU Wien)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7b1dd95f-4f16-4cbf-93d6-aad7952bbbef/
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DESCRIPTION:Talk:Title TBC
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BEGIN:VEVENT
SUMMARY:Title TBC
DTSTART;VALUE=DATE-TIME:20230130T140000Z
DTEND;VALUE=DATE-TIME:20230130T150000Z
UID:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
DESCRIPTION:\nSpeakers:\nDavid Croydon (RIMS\, Kyoto University)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
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DESCRIPTION:Talk:Title TBC
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BEGIN:VEVENT
SUMMARY:Title TBC
DTSTART;VALUE=DATE-TIME:20230116T140000Z
DTEND;VALUE=DATE-TIME:20230116T150000Z
UID:https://talks.ox.ac.uk/talks/id/b01d5ddc-859b-4a44-a1a4-8e562ec2b091/
DESCRIPTION:\nSpeakers:\nNikolaos Fountoulakis (University of Birmingham)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b01d5ddc-859b-4a44-a1a4-8e562ec2b091/
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ACTION:display
DESCRIPTION:Talk:Title TBC
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BEGIN:VEVENT
SUMMARY:Convergence of genealogies through spinal decomposition - Félix F
outel-Rodier (University of Oxford)
DTSTART;VALUE=DATE-TIME:20221031T120000Z
DTEND;VALUE=DATE-TIME:20221031T130000Z
UID:https://talks.ox.ac.uk/talks/id/6b095162-04ab-44fe-b093-f8b724676ba0/
DESCRIPTION:Consider a branching process where each individual is endowed
with a heritable type that influences its reproductive success. In this pr
esentation I will outline a new approach to study the scaling limit of the
genealogy and distribution of types of such branching processes\, when lo
oked at a large time horizon. It relies on two main building blocks: 1) vi
ewing genealogies as random metric measure spaces in the Gromov-weak topol
ogy and 2) computing the Gromov-weak "moments" of the genealogy using a ma
ny-to-few formula. I will illustrate this approach on the simple example o
f multi-type Galton-Watson processes and discuss some more complex models
that we have been considering.\n\nThis is based on a joint work with Emman
uel Schertzer\, and another with Florin Boenkost and Emmanuel Schertzer.\n
Speakers:\nFélix Foutel-Rodier (University of Oxford)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/6b095162-04ab-44fe-b093-f8b724676ba0/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Convergence of genealogies through spinal decomposition -
Félix Foutel-Rodier (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Transitive closure in a polluted environment - Brett Kolesnik (Uni
versity of Oxford)
DTSTART;VALUE=DATE-TIME:20221010T120000
DTEND;VALUE=DATE-TIME:20221010T130000
UID:https://talks.ox.ac.uk/talks/id/1c42cc89-dd00-413c-82ce-300dbb4e3c60/
DESCRIPTION:We introduce a new percolation model\, inspired by recent work
s on jigsaw percolation\, graph bootstrap percolation\, and percolation in
polluted environments. We start with a collection of logical statements a
nd known implications\, as represented by an oriented graph G on n vertice
s. Then we attempt to logically complete the knowledge by transitivity\, h
owever\, a censor places restrictions\, represented by open and closed dir
ected edges. We show that if G is a connected graph of bounded degree\, an
d all other edges are open independently with probability p\, then the tra
nsition between sparse and full completion of open edges occurs at p_c = (
log n)^{-1/2+o(1)}. Joint work with Janko Gravner.\nSpeakers:\nBrett Koles
nik (University of Oxford)
LOCATION:Mathematical Institute (L1)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/1c42cc89-dd00-413c-82ce-300dbb4e3c60/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Transitive closure in a polluted environment - Brett Kole
snik (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branching annihilating random walks with local self-regulations -
Alice Callegaro (Mainz)
DTSTART;VALUE=DATE-TIME:20221121T120000Z
DTEND;VALUE=DATE-TIME:20221121T130000Z
UID:https://talks.ox.ac.uk/talks/id/657b1ee9-2ab3-48cd-866d-49a8cea4e491/
DESCRIPTION:Branching annihilating random walks are interacting particle s
ystems that appear as a natural mathematical tool to model the spread of a
population competing for spatial resources. The classical methods for pro
ving survival heavily rely on monotonicity properties of the system and ar
e therefore not applicable in this context. We consider a model on the lat
tice in which particles branch\, perform jumps within a certain radius of
their parent and are killed whenever they occupy the same site. We study t
he extinction and survival of the system under different parameter regimes
and prove results about the particle density on the survival cluster. Bas
ed on joint works with Nina Gantert (TU Munich)\, Matthias Birkner (Univer
sity of Mainz)\, Jiri Cérny (University of Basel) and Pascal Oswald (Uni
versity of Basel). \nSpeakers:\nAlice Callegaro (Mainz)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/657b1ee9-2ab3-48cd-866d-49a8cea4e491/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Branching annihilating random walks with local self-regul
ations - Alice Callegaro (Mainz)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heat kernel fluctuations for the three-dimensional uniform spannin
g tree - Satomi Watanabe (Kyoto)
DTSTART;VALUE=DATE-TIME:20221114T120000Z
DTEND;VALUE=DATE-TIME:20221114T130000Z
UID:https://talks.ox.ac.uk/talks/id/365bc810-6936-4677-bf9b-a28ec8b500ac/
DESCRIPTION:Heat kernel fluctuations have been observed in some random wal
ks in random environments. In this talk\, I will consider the three-dimens
ional uniform spanning tree (UST) as a random environment. I will first sh
ow the occurrence of log-logarithmic fluctuations around the leading order
for the volume of intrinsic balls in the UST. This is then used to obtain
similar fluctuations for the quenched heat kernel.\nSpeakers:\nSatomi Wat
anabe (Kyoto)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/365bc810-6936-4677-bf9b-a28ec8b500ac/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Heat kernel fluctuations for the three-dimensional unifor
m spanning tree - Satomi Watanabe (Kyoto)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limit of high-dimensional uniform spanning trees - Eleanor
Archer (Paris Nanterre)
DTSTART;VALUE=DATE-TIME:20221107T120000Z
DTEND;VALUE=DATE-TIME:20221107T130000Z
UID:https://talks.ox.ac.uk/talks/id/d7549332-6ed2-461a-bd9c-c14f08003038/
DESCRIPTION:A spanning tree of a finite connected graph G is a connected s
ubgraph of G that touches every vertex and contains no cycles. In this tal
k we will consider uniformly drawn spanning trees of ``high-dimensional''
graphs\, and show that\, under appropriate rescaling\, they converge in di
stribution as metric-measure spaces to Aldous' Brownian CRT. This extends
an earlier result of Peres and Revelle (2004) who previously showed a form
of finite-dimensional convergence. Based on joint works with Asaf Nachmia
s and Matan Shalev.\nSpeakers:\nEleanor Archer (Paris Nanterre)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d7549332-6ed2-461a-bd9c-c14f08003038/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limit of high-dimensional uniform spanning trees
- Eleanor Archer (Paris Nanterre)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limit of an adaptive contact process - Daniel Valesin (Uni
versity of Warwick)
DTSTART;VALUE=DATE-TIME:20221128T120000Z
DTEND;VALUE=DATE-TIME:20221128T130000Z
UID:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
DESCRIPTION:We introduce and study an interacting particle system evolving
on the d-dimensional torus \\Z^d_N. Each vertex of the torus can be eithe
r empty or occupied by an individual of a given type\; the space of all ty
pes is the positive real line. An individual of type \\lambda dies with ra
te one and gives birth at each neighbouring empty position with rate \\lam
bda. Moreover\, when the birth takes place\, the new individual is likely
to have the same type as the parent\, but has a small chance to be a mutan
t\; the mutation rate and law of the type of the mutant both depend on \\l
ambda. We consider the asymptotic behaviour of this process when the size
of the torus is taken to infinity and the overall rate of mutation tends t
o zero fast enough that mutations are sufficiently separated in time\, so
that the amount of time spent on configurations with more than one type be
comes negligible. We show that\, after a suitable projection (which extrac
ts just the dominant type from the configuration of individuals in the tor
us) and time scaling\, the process converges to a Markov jump process on t
he positive real lines\, whose rates we determine. Joint work with Adrián
González Casanova and András Tobias.\nSpeakers:\nDaniel Valesin (Univer
sity of Warwick)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/7453685b-814a-429b-884d-3ce4f01ad20e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limit of an adaptive contact process - Daniel Val
esin (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weaves\, webs and flows - Nic Freeman (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20221017T120000
DTEND;VALUE=DATE-TIME:20221017T130000
UID:https://talks.ox.ac.uk/talks/id/28e9ca1a-e041-4284-9ccd-27ea487424fc/
DESCRIPTION:We consider "weaves" - loosely\, a weave is a set of non-cross
ing cadlag paths that covers 1+1 dimensional space-time. Here\, we do not
require any particular distribution for the particle motions. Weaves are a
general class of random processes\, of which the Brownian web is a canoni
cal example\; just as Brownian motion is a canonical example of a (single)
random path. It turns out that the space of weaves has an interesting geo
metric structure in its own right\, which will be the focus of the talk. T
his structure provides key information that leads to an accessible theory
of weak convergence for general weaves. Joint work with Jan Swart.\nSpeake
rs:\nNic Freeman (University of Sheffield)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/28e9ca1a-e041-4284-9ccd-27ea487424fc/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Weaves\, webs and flows - Nic Freeman (University of Shef
field)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamically resampling random trees - Edward Crane (University of
Bristol)
DTSTART;VALUE=DATE-TIME:20220620T120000
DTEND;VALUE=DATE-TIME:20220620T130000
UID:https://talks.ox.ac.uk/talks/id/d7d11acc-ae41-4308-adf7-445185281838/
DESCRIPTION:In ongoing work with Erin Russell\, we are studying a directed
version of the mean field forest fire model that was introduced by Balazs
Rath and Balint Toth in 2009. This is not a realistic model of real-world
forest fires! Instead\, it is a mathematically tractable dynamic random g
raph model that displays self-organized criticality.\n\nIn the first half
of the talk\, we will explain a coupling between the directed and undirect
ed versions of this forest fire model\, and some consequences. For example
\, for suitable initial conditions\, we expect that the out-graph of a tag
ged vertex in the directed model is approximated by a critical multitype B
ienayme-Galton-Watson (BGW) tree. This tree evolves in time by growth even
ts and by pruning events whose rate at each vertex is type-dependent.\n\nI
n the second half of the talk\, we will look at some simpler dynamic rando
m tree processes of a similar flavour\, which have a single-type BGW tree
as their stationary law. For example\, consider a critical binary BGW tree
whose vertices carry independent exponential alarm clocks of rate 1. When
the clock at any vertex v rings at time t\, the entire subtree above v is
instantaneously resampled. This means that it is replaced with a new crit
ical binary BGW tree rooted at v\, which is independent of the history bef
ore time t. We show that a.s. there are no exceptional times at which this
dynamic critical tree is infinite. \nSpeakers:\nEdward Crane (University
of Bristol)
LOCATION:Mathematical Institute\, L5
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d7d11acc-ae41-4308-adf7-445185281838/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Dynamically resampling random trees - Edward Crane (Unive
rsity of Bristol)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universality in random growth processes - Sourav Sarkar (Universit
y of Cambridge)
DTSTART;VALUE=DATE-TIME:20220613T120000
DTEND;VALUE=DATE-TIME:20220613T130000
UID:https://talks.ox.ac.uk/talks/id/cbc6b809-eb37-45bb-86d9-e4c1502dcd4a/
DESCRIPTION:Universality in disordered systems has always played a central
role in the direction of research in Probability and Mathematical Physics
\, a classical example being the Gaussian universality class (the central
limit theorem). In this talk\, I will describe a different universality cl
ass for random growth models\, called the KPZ universality class. Since Ka
rdar\, Parisi and Zhang introduced the KPZ equation in their seminal paper
in 1986\, the equation has made appearances everywhere from bacterial gro
wth\, fire front\, coffee stain to the top edge of a randomized game of Te
tris\; and this field has become a subject of intense research interest in
Mathematics and Physics for the last 15 to 20 years. The random growth pr
ocesses that are expected to have the same scaling and asymptotic fluctuat
ions as the KPZ equation and converge to the universal limiting object cal
led the KPZ fixed point\, are said to lie in the KPZ universality class\,
though this KPZ universality conjecture has been rigorously proved for onl
y a handful of models till now. Here\, I will talk about some recent resul
ts on universal geometric properties of the KPZ fixed point and the underl
ying landscape and show that the KPZ equation and exclusion processes con
verge to the KPZ fixed point under the 1:2:3 scaling\, establishing the KP
Z universality conjecture for these models\, which were long-standing open
problems in this field.\n\nThe talk is based on joint works with Jeremy Q
uastel\, Balint Virag and Duncan Dauvergne.\n\nSpeakers:\nSourav Sarkar (U
niversity of Cambridge)
LOCATION:Mathematical Institute\, L5
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/cbc6b809-eb37-45bb-86d9-e4c1502dcd4a/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Universality in random growth processes - Sourav Sarkar (
University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limit of a branching process in a varying environment - Gu
illaume Conchon-Kerjan (University of Bath)
DTSTART;VALUE=DATE-TIME:20220606T120000
DTEND;VALUE=DATE-TIME:20220606T130000
UID:https://talks.ox.ac.uk/talks/id/3cc65a85-cdf0-4b94-98d9-8d01c0a9a59c/
DESCRIPTION:A branching process in varying environment (BPVE) is a Galton-
Watson tree whose offspring distribution can change at each generation. Th
e evolution of the size of successive generations when the process does no
t die out early has drawn a lot of attention in recent years\, both from t
he discrete and continuum points of view (the scaling limit being a modifi
ed Continuous State Branching Process).\n\nWe focus on the limiting geneal
ogical structure\, in the critical case (all distributions have offspring
mean 1). We show that under mild second moment assumptions on the sequence
of offspring distributions\, a BPVE conditioned to be large converges to
the Brownian Continuum Random Tree\, as in the standard Galton-Watson sett
ing. The varying environment adds asymmetry and dependencies in many place
s. This requires numerous changes to the usual arguments\, in particular f
or the height process\, for which we propose a simple and (to our knowledg
e) new interpretation. \n\nThis is joint work with Daniel Kious and Cécil
e Mailler.\nSpeakers:\nGuillaume Conchon-Kerjan (University of Bath)
LOCATION:Mathematical Institute\, L5
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3cc65a85-cdf0-4b94-98d9-8d01c0a9a59c/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limit of a branching process in a varying environ
ment - Guillaume Conchon-Kerjan (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the contact process in an evolving random environment - Anja St
urm (University of Göttingen)
DTSTART;VALUE=DATE-TIME:20220516T120000
DTEND;VALUE=DATE-TIME:20220516T130000
UID:https://talks.ox.ac.uk/talks/id/39ad6c9f-1581-4058-8633-336d40058330/
DESCRIPTION:Recently\, there has been increasing interest in interacting p
article systems on evolving random graphs\, respectively in time evolving
random environments. In this talk we will present some results on the cont
act process in a evolving (edge) random environment on (infinite) connecte
d and transitive graphs with bounded degrees. We assume that the evolving
random environment is described by an autonomous ergodic spin systems with
finite range\, for example by dynamical percolation. This background proc
ess determines which edges are open or closed for infections.\n\nMost cont
ribution to this class of models are very recent and we will give a short
overview. Our own resulsts concern the dependence of the critical infectio
n rate for survival on the random environment and on the initial configura
tion of the system. For the latter we state sufficient conditions such tha
t the initial configuration of the system has no influence on the phase tr
ansition between extinction and survival. We show that this phase transiti
on coincides with the phase transition between a trivial/non-trivial uppe
r invariant law. We also discuss the continuity properties of the surviva
l probability as well as conditions for complete convergence.\nFinally\, w
e touch upon considering the contact process on dynamical long range perc
olation and discuss some open problems\, conjecture and further research d
irections.\n\nThis is joint work with Marco Seiler (University of Götting
en).\n\nSpeakers:\nAnja Sturm (University of Göttingen)
LOCATION:Mathematical Institute (Lecture Room 4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/39ad6c9f-1581-4058-8633-336d40058330/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:On the contact process in an evolving random environment
- Anja Sturm (University of Göttingen)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:A guide to growing random geometries: making trees blossom and tri
angulations flip - Alessandra Caraceni (Scuola Normale Superiore\, Pisa)
DTSTART;VALUE=DATE-TIME:20220530T120000
DTEND;VALUE=DATE-TIME:20220530T130000
UID:https://talks.ox.ac.uk/talks/id/b629131c-59e2-447e-93e5-c046c3504a37/
DESCRIPTION:In this talk\, based on joint work with Alexandre Stauffer\, w
e will discuss the problem of providing "uniform growth schemes" for vario
us types of planar maps — namely\, of coupling a uniform map with n face
s with a uniform map with n+1 faces in such a way that the smaller map is
always obtained from the larger by collapsing a single face. We show that
uniform growth schemes exist for rooted 2p-angulations of the sphere and f
or rooted simple triangulations\, and briefly touch on some applications t
o mixing time questions for edge flip chains.\n\nSpeakers:\nAlessandra Car
aceni (Scuola Normale Superiore\, Pisa)
LOCATION:Mathematical Institute (Lecture Room 4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b629131c-59e2-447e-93e5-c046c3504a37/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:A guide to growing random geometries: making trees blosso
m and triangulations flip - Alessandra Caraceni (Scuola Normale Superiore\
, Pisa)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Characterising the Gaussian free field - Ellen Powell (Durham Univ
ersity)
DTSTART;VALUE=DATE-TIME:20220523T120000
DTEND;VALUE=DATE-TIME:20220523T130000
UID:https://talks.ox.ac.uk/talks/id/5f89dc11-1d39-42e3-b742-443c1abfdf15/
DESCRIPTION:I will discuss recent approaches to characterising the Gaussia
n free field in the plane\, and in higher dimensions. The talk will be bas
ed on joint work with Juhan Aru\, Nathanael Berestycki and Gourab Ray. \nS
peakers:\nEllen Powell (Durham University)
LOCATION:Mathematical Institute (Lecture Room 3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/5f89dc11-1d39-42e3-b742-443c1abfdf15/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Characterising the Gaussian free field - Ellen Powell (Du
rham University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Metastability for loss networks - Sam Olesker-Taylor (University o
f Bath)
DTSTART;VALUE=DATE-TIME:20220509T120000
DTEND;VALUE=DATE-TIME:20220509T130000
UID:https://talks.ox.ac.uk/talks/id/496d37fc-55ed-4f39-9e31-e2af1eb59d5c/
DESCRIPTION:We consider a fully-connected loss network with dynamic altern
ative routing\, each link of capacity K. Calls arrive to each link {i\,
j} at rate λ. If the link is full upon arrival\, a third node k is chosen
uniform and the call is routed via k: it uses a unit of capacity on both
{i\, k} and {k\, j} if both have spare capacity\; otherwise\, the call
is lost.\n\nWe analyse the asymptotics of the mixing time of this process
\, depending on the traffic intensity α := λ/K. In particular\, we d
etermine a phase transition at an explicit threshold α_c: there is fast m
ixing if α < α_c or α > 1\, but metastability if α_c < α
< 1.\nSpeakers:\nSam Olesker-Taylor (University of Bath)
LOCATION:Mathematical Institute (Lecture Room 4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/496d37fc-55ed-4f39-9e31-e2af1eb59d5c/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Metastability for loss networks - Sam Olesker-Taylor (Uni
versity of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limit distributions of branching Markov chains - Vadim Kaimanovich
(Ottawa)
DTSTART;VALUE=DATE-TIME:20220304T120000Z
DTEND;VALUE=DATE-TIME:20220304T130000Z
UID:https://talks.ox.ac.uk/talks/id/dd2b1d39-cb55-4599-a90f-b36edd6c1cae/
DESCRIPTION:The talk is based on joint work with Wolfgang Woess. There is
a large body\nof literature devoted to the quantitative aspects of branchi
ng random\nwalks on the additive group of real numbers and to the behaviou
r of the\nassociated martingales. In what concerns more general state spac
es rich\nenough to have a non-trivial topological boundary at infinity (li
ke\, for\ninstance\, infinite trees)\, it is natural to ask about the limi
t behaviour\nof the branching populations in geometric terms. Non-trivial
limit sets of\nrandom population sequences were first exhibited by Liggett
(1996) and\nlater studied in similar situations by Hueter - Lalley (2000)
\, Benjamini -\nMuller (2012)\, \nCandellero – Roberts (2015) and Hutchc
roft (2020).\n\nWe are looking at branching random walks from a different
and apparently\nnovel angle. We are interested in the random limit boundar
y measures\narising from the uniform distributions on sample populations.
Unlike with\nthe limit sets\, the very existence of the limit measures is
already a\nnon-trivial problem. We consider and solve this problem in two
different\nsetups: in the topological one (when the boundary of the state
space is\nprovided by a certain compactification) and in the measure-theor
etical one\n(when we are dealing with the Poisson or exit boundary of the
underlying\nMarkov chain on the state space).\nSpeakers:\nVadim Kaimanovic
h (Ottawa)
LOCATION:Mathematical Institute\, L4
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/dd2b1d39-cb55-4599-a90f-b36edd6c1cae/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Limit distributions of branching Markov chains - Vadim Ka
imanovich (Ottawa)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mixing times for the TASEP on the circle - Dominik Schmid (Bonn /
Princeton)
DTSTART;VALUE=DATE-TIME:20220228T110000Z
DTEND;VALUE=DATE-TIME:20220228T120000Z
UID:https://talks.ox.ac.uk/talks/id/f916bd99-22ed-4a18-8941-821a78fdb3be/
DESCRIPTION:The exclusion process is one of the best-studied examples of a
n interacting particle system. In this talk\, we consider simple exclusion
processes on finite graphs. We give an overview over some recent results
on the mixing time of the totally asymmetric simple exclusion process (TAS
EP). In particular\, we provide bounds on the mixing time of the TASEP on
the circle\, using a connection to periodic last passage percolation. This
talk is based on joint work with Allan Sly (Princeton). \nSpeakers:\nDomi
nik Schmid (Bonn / Princeton)
LOCATION:Mathematical Institute\, L4
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/f916bd99-22ed-4a18-8941-821a78fdb3be/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Mixing times for the TASEP on the circle - Dominik Schmid
(Bonn / Princeton)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limits of multi-type Markov Branching Trees - Robin Stephe
nson (University of Sheffield)
DTSTART;VALUE=DATE-TIME:20220216T120000Z
DTEND;VALUE=DATE-TIME:20220216T130000Z
UID:https://talks.ox.ac.uk/talks/id/b30df359-9194-458b-9d6c-e1f17ef941fd/
DESCRIPTION:Consider a population where individuals have two characteristi
cs: a size\, which is a positive integer\, and a type\, which is a member
of a finite set. This population reproduces in a Galton-Watson fashion\, w
ith one additional condition: given that an individual has size $n$\, the
sum of the sizes of its children is less than or equal to n. We call multi
-type Markov branching tree the family tree of such a population.\n\nWe sh
ow that under some assumptions about the splitting rates\, Markov branchin
g trees have scaling limits in distribution which are self-similar fragmen
tation trees\, monotype or multi-type.\n\nWe then give two applications: t
he scaling limits of some growth models of random trees\, and new results
on the scaling limits of multi-type Galton-Watson trees.\n\nThis is joint
work with Bénédicte Haas.\n\nSpeakers:\nRobin Stephenson (University of
Sheffield)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b30df359-9194-458b-9d6c-e1f17ef941fd/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limits of multi-type Markov Branching Trees - Rob
in Stephenson (University of Sheffield)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random walk on the simple symmetric exclusion process - Daniel Kio
us (University of Bath)
DTSTART;VALUE=DATE-TIME:20220126T120000Z
DTEND;VALUE=DATE-TIME:20220126T130000Z
UID:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
DESCRIPTION:In a joint work with Marcelo R. Hilário and Augusto Teixeira\
, we investigate the long-term behavior of a random walker evolving on top
of the simple symmetric exclusion process (SSEP) at equilibrium. At each
jump\, the random walker is subject to a drift that depends on whether it
is sitting on top of a particle or a hole. The asymptotic behavior is expe
cted to depend on the density ρ in [0\, 1] of the underlying SSEP.\nOur f
irst result is a law of large numbers (LLN) for the random walker for all
densities ρ except for at most two values ρ− and ρ+ in [0\, 1]\, wher
e the speed (as a function of the density) possibly jumps from\, or to\, 0
. \nSecond\, we prove that\, for any density corresponding to a non-zero s
peed regime\, the fluctuations are diffusive and a Central Limit Theorem h
olds.\nFor the special case in which the density is 1/2 and the jump distr
ibution on an empty site and on an occupied site are symmetric to each oth
er\, we prove a LLN with zero limiting speed.\nOur main results extend to
environments given by a family of independent simple symmetric random walk
s in equilibrium.\nSpeakers:\nDaniel Kious (University of Bath)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Random walk on the simple symmetric exclusion process - D
aniel Kious (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Local and global behavior of the subcritical contact process - Dr
Leonardo Rolla (University of Warwick)
DTSTART;VALUE=DATE-TIME:20220223T120000Z
DTEND;VALUE=DATE-TIME:20220223T130000Z
UID:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
DESCRIPTION:We will describe the scaling limit of the subcritical contact
process in terms of a marked Poisson point process and a quasi-stationary
distribution\, and discuss the question of uniqueness of the QSD in this a
nd other contexts. Based on joint works with E. Andjel\, F. Ezanno and P.
Groisman\, with Aurelia Deshayes\, and with F. Arrejoría and P. Groisman.
\nSpeakers:\nDr Leonardo Rolla (University of Warwick)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/881d7822-7143-45d1-b982-2a6350e6efb4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Local and global behavior of the subcritical contact proc
ess - Dr Leonardo Rolla (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exchangeability\, mixtures and continuum random trees - Minmin Wan
g (University of Sussex)
DTSTART;VALUE=DATE-TIME:20220209T120000Z
DTEND;VALUE=DATE-TIME:20220209T130000Z
UID:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
DESCRIPTION:I’ll start with a quick review on some classical results on
exchangeability\, particularly Kallenberg’s theorem on the canonical for
m of an exchangeable process on [0\, 1]. The 2005 work of Aldous\, Miermon
t and Pitman reveals a close connection between exchangeable processes and
a class of continuum random tree called inhomogeneous continuum random tr
ees (ICRT)\, leading to their claim that Lévy trees are mixtures of ICRT.
I’ll present a proof in the case of stable Lévy trees\, based upon a
new way of constructing continuum random trees that work both for stable t
rees and ICRT.\nSpeakers:\nMinmin Wang (University of Sussex)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/44d82120-1076-4284-8730-9bc70119368d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Exchangeability\, mixtures and continuum random trees - M
inmin Wang (University of Sussex)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hybrid zones and the effect of barriers - Ian Letter (Department o
f Statistics)
DTSTART;VALUE=DATE-TIME:20211115T120000Z
DTEND;VALUE=DATE-TIME:20211115T130000Z
UID:https://talks.ox.ac.uk/talks/id/cfc4a824-309d-4d81-a25e-722b8a644727/
DESCRIPTION:Hybrid zones are narrow regions in which two distinct types of
individuals reproduce and produce offspring of mixed type. Some mathemati
cal models conclude that hybrid zones of populations with asymmetric selec
tion against heterozygotes evolve\, when correctly rescaled\, as mean curv
ature flow plus a constant flow. This conclusion rests on modelling the de
nsity of a particular allele as the solution of a partial differential equ
ation in the euclidean space\, proving the result in that deterministic se
tting and finally showing the presence of genetic drift does not disrupt t
he conclusion. In this talk\, I will sketch the main ingredients to adapt
this result to capture an effect one would see in a real-life population\;
the presence of barriers. Barriers refer to environmental obstacles that
prevent individuals from invading certain zones. Mathematically this trans
lates into studying the dynamics in a subset of the euclidean space with r
eflecting conditions on the boundary. We show that in a particular family
of domains there is a phase transition\; if the domain presents an "openin
g bigger" than an explicit constant there is an invasion of the fittest ty
pe\, but if the opening is smaller than said constant then there is coexis
tence between the two types of individuals. We also mention how the presen
ce of genetic drift (modelled by a Spatial-Lambda-Fleming Viot type proces
s) may affect these results. This is work under the supervision of Alison
Etheridge.\nSpeakers:\nIan Letter (Department of Statistics)
LOCATION:Department of Statistics\, IT Suite
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/cfc4a824-309d-4d81-a25e-722b8a644727/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Hybrid zones and the effect of barriers - Ian Letter (Dep
artment of Statistics)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Large degrees yield short trees - Serte Donderwinkel (Department o
f Statistics\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20211101T120000Z
DTEND;VALUE=DATE-TIME:20211101T130000Z
UID:https://talks.ox.ac.uk/talks/id/e692e213-9171-4d9d-9e63-bdeb2a607656/
DESCRIPTION:I will speak about results from an ongoing project with Louigi
Addario-Berry. I will present non-asymptotic\, universal height bounds fo
r random combinatorial trees. We use these results to show height bounds o
n conditioned Bienaymé trees and simply generated trees. Moreover\, I wil
l introduce a stochastic domination result for combinatorial trees\, imply
ing that binary trees are stochastically the tallest. These results are ba
sed on a new bijection between trees and sequences that got introduced in
a joint work with Louigi Addario-Berry\, Mickaël Maazoun and James Martin
.\n\nSpeakers:\nSerte Donderwinkel (Department of Statistics\, University
of Oxford)
LOCATION:Department of Statistics\, Large Lecture Theatre
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e692e213-9171-4d9d-9e63-bdeb2a607656/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Large degrees yield short trees - Serte Donderwinkel (Dep
artment of Statistics\, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random linear extensions of posets - Igor Pak (UCLA)
DTSTART;VALUE=DATE-TIME:20200302T120000Z
DTEND;VALUE=DATE-TIME:20200302T130000Z
UID:https://talks.ox.ac.uk/talks/id/0ea4c00f-a5ea-4753-8205-f0dc2a99fde7/
DESCRIPTION:Linear extensions of a poset $(X\, \\prec)$ of size $n$ are in
creasing bijections from $X$ to $\\{1\,...\,n\\}$. These linear extension
generalize Young tableaux and various multi-dimensional random walks model
s. We will survey what is known about the asymptotic and probabilistic beh
avior of linear extensions and present our recent work on the subject. The
talk is aimed at a general audience. \nSpeakers:\nIgor Pak (UCLA)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/0ea4c00f-a5ea-4753-8205-f0dc2a99fde7/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Random linear extensions of posets - Igor Pak (UCLA)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Critical scaling limit of the random intersection graph - Lorenzo
Federico (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200203T120000Z
DTEND;VALUE=DATE-TIME:20200203T130000Z
UID:https://talks.ox.ac.uk/talks/id/fbe11fd2-9219-4266-a3c4-46bbe6c48b0e/
DESCRIPTION:In this talk\, we prove a scaling limit for the size (both in
terms of vertices and edges) of the largest components of a critical rando
m intersection graph in which each individual is assigned to each communit
y with a uniform probability p\, all independently of each other. We show
that the order of magnitude of the largest component depends significantly
on the asymptotic behaviour of the ratio between the number of individual
s and communities\, while the limit random variables to which component si
zes converge after rescaling are the same as in the Erdos-Renyi Random Gra
ph. We further discuss how this result relates to the known scaling limits
of critical inhomogeneous random graphs.\nSpeakers:\nLorenzo Federico (Un
iversity of Warwick)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/fbe11fd2-9219-4266-a3c4-46bbe6c48b0e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Critical scaling limit of the random intersection graph -
Lorenzo Federico (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Household epidemic models and McKean-Vlasov Poisson driven SDEs -
Raphaël Forien (INRA\, Avignon)
DTSTART;VALUE=DATE-TIME:20200224T120000Z
DTEND;VALUE=DATE-TIME:20200224T130000Z
UID:https://talks.ox.ac.uk/talks/id/a6b59c04-5fc4-4edb-9269-7b69eac44e69/
DESCRIPTION:In this talk I will present an epidemic model where susceptibl
e and infected individuals are distributed in discrete households of finit
e size. Infected individuals can either infect other individuals in the sa
me household or individuals chosen uniformly in the whole population. When
the number of households tends to infinity\, we obtain a limit for the ep
idemic process given in terms of a nonlinear Markov process which solves a
McKean-Vlasov Poisson driven SDE. We also prove a propagation of chaos re
sult. Finally\, we define a basic reproduction number R0\, and show that i
f R0>1\, then the nonlinear Markov process has a unique non trivial ergodi
c invariant probability measure (i.e. the epidemic spreads to a large prop
ortion of the population with positive probability)\, whereas if R0<=1\, t
he non-linear Markov process converges to 0 as t tends to infinity (the ep
idemic quickly dies out). To conclude I will mention some results on the f
luctuations of the epidemic process.\n\nThis is joint work with Étienne P
ardoux.\nSpeakers:\nRaphaël Forien (INRA\, Avignon)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/a6b59c04-5fc4-4edb-9269-7b69eac44e69/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Household epidemic models and McKean-Vlasov Poisson drive
n SDEs - Raphaël Forien (INRA\, Avignon)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scaling limits of finitely specified permutation classes - Mickaë
l Maazoun (ENS Lyon)
DTSTART;VALUE=DATE-TIME:20200217T120000Z
DTEND;VALUE=DATE-TIME:20200217T130000Z
UID:https://talks.ox.ac.uk/talks/id/76cda1bb-51ad-46c2-9b2d-e34ba488e0d4/
DESCRIPTION:The subject of pattern-avoiding permutations is a classic of e
numerative combinatorics\, still rich of interesting open problems. We ado
pt a probabilistic point of view: What does the diagram of a large permuta
tion in a pattern-avoiding class typically look like? Generalising previo
us results\, we consider classes with nice encodings by multi-type trees.
We show that they converge either to "Brownian separable permutons" or det
erministic limit shapes.\n\nI will explain how we use analytic combinatori
cs to study the scaling limit of the encoding trees without completely los
ing information about types and degrees of branch points.\n\nIf I have som
e time left\, I will talk about some computations that we can perform on t
he limiting objects\, with interesting consequences in the discrete.\n\nTh
is is joint work with F. Bassino\, M. Bouvel\, V. Féray\, L. Gerin\, A. P
ierrot -- arXiv:1903.07522.\nSpeakers:\nMickaël Maazoun (ENS Lyon)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/76cda1bb-51ad-46c2-9b2d-e34ba488e0d4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Scaling limits of finitely specified permutation classes
- Mickaël Maazoun (ENS Lyon)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Where are the faraway particles of the branching Brownian motion i
n dimension d? - Roman Stasiński (Department of Statistics\, University o
f Oxford)
DTSTART;VALUE=DATE-TIME:20191125T120000Z
DTEND;VALUE=DATE-TIME:20191125T130000Z
UID:https://talks.ox.ac.uk/talks/id/963053ca-f60f-46cd-b218-fde0b846d6d5/
DESCRIPTION:Branching Brownian motion is a model in which independent part
icles move as Brownian motions and branch at rate 1. Its behavior\, and in
particular the description of what happens near its extremal particles (t
he ones furthest away from the origin) is by now well understood in\ndimen
sion 1. By contrast\, not much is known about the multidimensional case.\n
\nIn this talk I will present the first step towards the goal of obtaining
the limiting extremal point process for the branching Brownian motion in\
nhigher dimensions. This involves in particular finding an analogue of the
so-called derivative martingale\, which plays a crucial role in d=1\,\nan
d studying its convergence.\n \nBased on a joint work with Bastien Mallein
(Université Paris 13).\nSpeakers:\nRoman Stasiński (Department of Stati
stics\, University of Oxford)
LOCATION:L4
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/963053ca-f60f-46cd-b218-fde0b846d6d5/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Where are the faraway particles of the branching Brownian
motion in dimension d? - Roman Stasiński (Department of Statistics\, Uni
versity of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The depth first search exploration of a supercritical configuratio
n model - Laurent Ménard (Université Paris Nanterre)
DTSTART;VALUE=DATE-TIME:20191121T100000Z
DTEND;VALUE=DATE-TIME:20191121T110000Z
UID:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
DESCRIPTION:We consider large random graphs with a given degree sequence.
In the sparse regime where the degree sequence converges to a probability
distribution\, the model has a phase transition for the existence of a mac
roscopic connected component. In this talk\, we will study the depth first
search algorithm in the supercritical regime. In particular\, we will see
that the evolution of the empirical degree distribution of the unexplored
vertices has a fluid limit which is driven by an infinite system of diffe
rential equations. Surprisingly\, this system admits an explicit solution
in terms of the initial degree distribution. This in turn allows to prove
that the renormalised contour process of the exploration has a determinist
ic profile for which we can give an explicit parametric representation. Th
e height of this curve gives information about long simple paths in the gr
aph.\nSpeakers:\nLaurent Ménard (Université Paris Nanterre)
LOCATION:24-29 St Giles' (Department of Statistics\, LG.01 (Large Lecture
Theatre))\, 24-29 St Giles' OX1 3LB
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b99e823e-182d-4f5e-88be-387c8632ce72/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The depth first search exploration of a supercritical con
figuration model - Laurent Ménard (Université Paris Nanterre)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Order of the variance in the discrete Hammersley process - Nicos G
eorgiou (University of Sussex)
DTSTART;VALUE=DATE-TIME:20191118T120000Z
DTEND;VALUE=DATE-TIME:20191118T130000Z
UID:https://talks.ox.ac.uk/talks/id/546181e7-31a9-4197-b8a7-58a5163e7e59/
DESCRIPTION:We discuss the order of the variance on a lattice analogue of
the Hammersley process\, for which the environment on each site has indepe
ndent\, Bernoulli distributed values. The last passage time is the maximu
m number of Bernoulli points that can be collected on a piecewise linear p
ath\, where each segment has strictly positive but finite slope.\n\nFor th
is model the shape function exhibits two flat edges and we study the order
of the variance in directions that fall in the flat edge\, in directions
that approximate the edge of the flat edge\, and in directions in the stri
ctly concave section of the shape for the i.i.d. model and for the associa
ted equilibrium model with boundaries. If time permitting\, we will discu
ss the shape function and variance in some inhomogeneous models as well. \
n\nThis is an exposition of several works with Janosch Ortmann\, Elnur Emr
ah and Federico Ciech.\nSpeakers:\nNicos Georgiou (University of Sussex)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/546181e7-31a9-4197-b8a7-58a5163e7e59/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Order of the variance in the discrete Hammersley process
- Nicos Georgiou (University of Sussex)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sparse graphs using exchangeable random measures: Models\, propert
ies and applications - François Caron (Department of Statistics\, Univers
ity of Oxford)
DTSTART;VALUE=DATE-TIME:20191111T120000Z
DTEND;VALUE=DATE-TIME:20191111T130000Z
UID:https://talks.ox.ac.uk/talks/id/f9f19da2-620c-4a5e-9fe6-211327a00b7e/
DESCRIPTION:In the talk I will present the class of random graphs based on
exchangeable random measures. Such class allows to model networks which a
re either dense or sparse\, that is where the number of edges scales subqu
adratically with the number of nodes. For some values of its parameters\,
it generates scale-free networks with power-law exponent between 1 and 2.
I will present the general construction\, a representation theorem for suc
h construction due to Kallenberg\, and discuss its sparsity\, power-law an
d transitivity properties. Then I will introduce a specific model within t
his framework that allows to capture sparsity/heavy-tailed degree distribu
tions as well as latent overlapping community structure\, and a Markov cha
in Monte Carlo algorithm for posterior inference with this model. Experime
nts are done on two real-world networks\, showing the usefulness of the ap
proach for network analysis. \n\nBased on joint work with Emily Fox\, Adri
en Todeschini\, Xenia Miscouridou\, Judith Rousseau\, Francesca Panero.\nS
peakers:\nFrançois Caron (Department of Statistics\, University of Oxford
)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/f9f19da2-620c-4a5e-9fe6-211327a00b7e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Sparse graphs using exchangeable random measures: Models\
, properties and applications - François Caron (Department of Statistics\
, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotics of discrete β-corners processes via discrete loop equ
ations - Alisa Knizel (Columbia University\, New York)
DTSTART;VALUE=DATE-TIME:20191104T120000Z
DTEND;VALUE=DATE-TIME:20191104T130000Z
UID:https://talks.ox.ac.uk/talks/id/357d7fce-9664-4aef-92eb-6127c8aa2c79/
DESCRIPTION:We introduce and study stochastic particle ensembles which are
natural discretizations of general β-corners processes. We prove that un
der technical assumptions on a general analytic potential the global fluct
uations for the difference between two adjacent levels are asymptotically
Gaussian. The covariance is universal and remarkably differs from its coun
terpart in random matrix theory. Our main tools are certain novel algebrai
c identities that are multi-level analogues of the discrete loop equations
. Based on joint work with Evgeni Dimitrov (Columbia University)\nSpeakers
:\nAlisa Knizel (Columbia University\, New York)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/357d7fce-9664-4aef-92eb-6127c8aa2c79/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Asymptotics of discrete β-corners processes via discrete
loop equations - Alisa Knizel (Columbia University\, New York)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keep the particles -- CANCELLED - Tom Kurtz (Madison-Wisconsin)
DTSTART;VALUE=DATE-TIME:20191021T120000
DTEND;VALUE=DATE-TIME:20191021T130000
UID:https://talks.ox.ac.uk/talks/id/ade45483-a2e9-49ec-b857-bb949c66f46e/
DESCRIPTION:\nStatus: This talk has been cancelled\nSome of the basic idea
s and methodology of what has been called the "bring back the particles"
approach to infinite population limits will be described. The approach is
perhaps better described as "don't let the particles get away in the first
place" or simply "keep the particles". In many areas (for example\, popul
ation biology. statistical physics\, queueing)\, models of large numbers o
f interacting entities (particles) are considered as the number of particl
es tends to infinity. Classically\, the approach has been to consider the
normalized empirical measure determined by the particles\, argue that the
empirical measure must converge as the size of the system tends to infinit
y\, and then identify the limiting measure as the solution of a PDE or SPD
E\, a measure-valued stochastic process\, etc. "Keep the particles" says t
hat the limit of finite systems as the number of particles goes to infinit
y should be an infinite system. The classical McKean-Vlasov model will be
considered along with a closely related model of asset prices. Time permit
ting\, using the approach to derive filtering equations will be discussed.
\nSpeakers:\nTom Kurtz (Madison-Wisconsin)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/ade45483-a2e9-49ec-b857-bb949c66f46e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Keep the particles -- CANCELLED - Tom Kurtz (Madison-Wisc
onsin)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hit and miss with the density of the (α\,β)-superprocess - Thoma
s Hughes (UBC)
DTSTART;VALUE=DATE-TIME:20191014T120000
DTEND;VALUE=DATE-TIME:20191014T130000
UID:https://talks.ox.ac.uk/talks/id/6c1fbe4e-7273-4fd6-a429-277d47f57ade/
DESCRIPTION:The (α\,β)-superprocess is a spatial branching model associa
ted to an α-stable spatial motion and a (1+β)-stable branching mechanism
. Formally\, it is a measure-valued Markov process\, but this talk concer
ns the absolutely continuous parameter regime\, in which the random measur
e has a density. After introducing this process and some classical results
\, I will discuss some newly proven path properties of the density. These
include (i) strict positivity of the density at a fixed time (for certain
values of α and β) and (ii) a classification of the measures which the d
ensity “charges” almost surely\, and of the measures which the density
fails to charge with positive probability\, when conditioned on survival.
The duality between the superprocess and a fractional PDE is central to o
ur method\, and I will discuss how the probabilistic statements above corr
espond to new results about solutions to the PDE.\n\nSpeakers:\nThomas Hug
hes (UBC)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/6c1fbe4e-7273-4fd6-a429-277d47f57ade/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Hit and miss with the density of the (α\,β)-superproces
s - Thomas Hughes (UBC)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Critical scaling limit of the random intersection graph -- POSTPON
ED TO NEXT TERM - Lorenzo Federico (University of Warwick)
DTSTART;VALUE=DATE-TIME:20191125T120000Z
DTEND;VALUE=DATE-TIME:20191125T130000Z
UID:https://talks.ox.ac.uk/talks/id/e8763c31-3d03-442d-b26f-a6d471576a7e/
DESCRIPTION:\nStatus: This talk has been cancelled\nIn this talk\, we prov
e a scaling limit for the size (both in terms of vertices and edges) of th
e largest components of a critical random intersection graph in which each
individual is assigned to each community with a uniform probability p\, a
ll independently of each other. We show that the order of magnitude of the
largest component depends significantly on the asymptotic behaviour of th
e ratio between the number of individuals and communities\, while the limi
t random variables to which component sizes converge after rescaling are t
he same as in the Erdos-Renyi Random Graph. We further discuss how this re
sult relates to the known scaling limits of critical inhomogeneous random
graphs.\nSpeakers:\nLorenzo Federico (University of Warwick)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e8763c31-3d03-442d-b26f-a6d471576a7e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Critical scaling limit of the random intersection graph -
- POSTPONED TO NEXT TERM - Lorenzo Federico (University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exceptional times of transience for a dynamical random walk - Matt
hew Roberts (University of Bath)
DTSTART;VALUE=DATE-TIME:20191028T120000Z
DTEND;VALUE=DATE-TIME:20191028T130000Z
UID:https://talks.ox.ac.uk/talks/id/30ad2bdb-e190-4cae-924d-3f2848081495/
DESCRIPTION:We define a dynamical simple symmetric random walk in one dime
nsion\, and show that there almost surely exist exceptional times at which
the walk tends to infinity. In fact the set of such times has Hausdorff d
imension 1/2 almost surely. This is in contrast to the usual dynamical sim
ple symmetric random walk in one dimension\, for which such exceptional ti
mes are known not to exist. This is joint work with Martin Prigent.\nSpeak
ers:\nMatthew Roberts (University of Bath)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/30ad2bdb-e190-4cae-924d-3f2848081495/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Exceptional times of transience for a dynamical random wa
lk - Matthew Roberts (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Near-critical percolation with heavy-tailed impurities - Pierre No
lin (City University of Hong Kong)
DTSTART;VALUE=DATE-TIME:20190624T120000
DTEND;VALUE=DATE-TIME:20190624T130000
UID:https://talks.ox.ac.uk/talks/id/fa62e391-c8b4-4630-bdf2-ade077c2f6cd/
DESCRIPTION:Consider a "nice" planar lattice\, such as the square or the t
riangular lattice. We introduce the following percolation model. First\, r
egions ("impurities") are removed from the lattice\, in some independent f
ashion\, and we then consider site percolation on the remaining vertices.
The mentioned impurities are not only microscopic\, but also allowed to be
mesoscopic ("heavy-tailed"\, in some sense).\n\nWe are typically interest
ed in whether\, on the randomly "perforated" lattice\, the connectivity pr
operties of percolation remain of the same order as without impurities\, f
or values of the percolation parameter close to the critical value. This g
eneralizes a celebrated result by Kesten for near-critical percolation (th
at can be viewed as critical percolation with single-site impurities).\n\n
This generalization arises naturally when studying models of forest fires
(or epidemics). Our results for percolation with impurities are instrument
al in analyzing the behavior of such processes near and beyond the critica
l time (i.e. the time after which\, in the absence of fires\, infinite con
nected components would emerge).\n\nThis talk is based on a joint work wit
h Rob van den Berg (CWI and VU\, Amsterdam).\n\nSpeakers:\nPierre Nolin (C
ity University of Hong Kong)
LOCATION:Mathematical Institute (C4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/fa62e391-c8b4-4630-bdf2-ade077c2f6cd/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Near-critical percolation with heavy-tailed impurities -
Pierre Nolin (City University of Hong Kong)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalized disconnection exponents for Brownian loop-soups - Wei
Qian (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20190624T140000
DTEND;VALUE=DATE-TIME:20190624T150000
UID:https://talks.ox.ac.uk/talks/id/d8aed3f5-23c2-4e49-9039-f9f2b95f76d7/
DESCRIPTION:We study the question of whether there exist double points on
the boundaries of clusters in Brownian loop-soups — an object introduced
by Lawler and Werner in 2004. This question is closely related to our ear
lier works (with Werner) on the decomposition of Brownian loop-soup cluste
rs. More concretely\, we introduce a notion of disconnection exponents whi
ch generalizes the Brownian disconnection exponents derived by Lawler\, Sc
hramm and Werner in 2001. By computing the generalized disconnection expon
ents\, we can predict the dimension of multiple points on the cluster boun
daries in loop-soups. However\, for the critical intensity of loop-soup\,
the dimension of double points on the cluster boundaries appears to be zer
o\, leaving the open problem of whether such points exist for the critical
loop-soup.\nSpeakers:\nWei Qian (University of Cambridge)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d8aed3f5-23c2-4e49-9039-f9f2b95f76d7/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Generalized disconnection exponents for Brownian loop-sou
ps - Wei Qian (University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simultaneous migration in the seed bank coalescent - Maite Wilke B
erenguer (TU Berlin)
DTSTART;VALUE=DATE-TIME:20190610T120000
DTEND;VALUE=DATE-TIME:20190610T130000
UID:https://talks.ox.ac.uk/talks/id/e6c58cfe-5c78-4899-aac1-3ce2740f782b/
DESCRIPTION:The geometric seed bank model was introduced to describe the e
volution of a population with active and dormant forms (`seeds') on a stru
cture Markovian in both directions of time\, whose limiting objects posses
the advantageous property of being moment duals of each other: The (biall
elic) Fisher-Wright diffusion with seed bank component describing the freq
uency of a given type of alleles forward in time and a new coalescent str
ucture named the seed bank coalescent describing the genealogy backwards i
n time.\nIn this talk more recent results on extensions of this model will
be discussed\, focusing on the seed bank model \\emph{with simultaneous m
igration}: in addition to the \\emph{spontaneous} migration modeled before
\, where individuals decided to migrate independently of each other\, corr
elated migration where several individuals become dormant (or awake) simul
taneously is included. In particular\, we will discuss the effect of the c
orrelation on the property of coming down from infinity.\n\nThis is joint
work with J. Blath (TU Berlin)\, A. González Casanova (UNAM)\, and N
. Kurt (TU Berlin).\nSpeakers:\nMaite Wilke Berenguer (TU Berlin)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e6c58cfe-5c78-4899-aac1-3ce2740f782b/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Simultaneous migration in the seed bank coalescent - Mait
e Wilke Berenguer (TU Berlin)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tales of Random Projections - Kavita Ramanan (Brown University)
DTSTART;VALUE=DATE-TIME:20190528T120000
DTEND;VALUE=DATE-TIME:20190528T130000
UID:https://talks.ox.ac.uk/talks/id/0cb9b171-07b2-434d-8f2e-eea8bff47784/
DESCRIPTION:The interplay between geometry and probability in high-dimensi
onal spaces is an active subject of current research. Classical theorems i
n probability theory such as the central limit theorem and Cramer’s theo
rem can be viewed as providing information about certain scalar projection
s of high-dimensional product measures. In this talk we will describe th
e behavior of random projections of more general (possibly non-product) hi
gh-dimensional measures\, which are of interest in diverse fields\, rangin
g from asymptotic convex geometry to high-dimensional statistics. Althou
gh the study of (typical) projections of high-dimensional measures dates b
ack to Borel\, only recently has a theory begun to emerge\, which in parti
cular identifies the role of certain geometric assumptions that lead to be
tter behaved projections. A particular question of interest is to identi
fy what properties of the high-dimensional measure are captured by its lo
wer-dimensional projections. While fluctuations of these projections hav
e been studied over the past decade\, we describe more recent work on the
tail behavior of multidimensional projections\, and associated conditional
limit theorems. This is based on joint work with Steven Soojin Kim and
Nina Gantert.\nSpeakers:\nKavita Ramanan (Brown University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/0cb9b171-07b2-434d-8f2e-eea8bff47784/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Tales of Random Projections - Kavita Ramanan (Brown Unive
rsity)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiple merger coalescents: truncated offspring distributions\, l
arge sample sizes\, and bottlenecks - Jonathan Chetwynd-Diggle (University
of Oxford)
DTSTART;VALUE=DATE-TIME:20190520T120000
DTEND;VALUE=DATE-TIME:20190520T130000
UID:https://talks.ox.ac.uk/talks/id/14ab186f-d324-4b6a-b6fd-cb1cf5797eb0/
DESCRIPTION:Recent genetic profiling of 30\,000 Icelandic cod have produce
d data which suggests that a Lambda coalescent rather than Kingman's coale
scent is a suitable model for their ancestral lineages. We will discuss a
class of population models analysed in Schweinsberg\, 2003\, along with i
ts applicability as a population model. We have also looked into issues wh
ich arise in using coalescent models for the large sample sizes modern seq
uencing technology has enabled. Work by Wakeley and Takahashi\, 2003\, sho
wed a breakdown in the coalescent approximation when the sample size is on
the same order as effective population size. We will show heuristic argum
ents that show why the breakdown appears so late in the Kingman regime and
extend the arguments to the Lambda regime. Joint work with Bjarki Eldon a
nd Alison Etheridge.\nSpeakers:\nJonathan Chetwynd-Diggle (University of O
xford)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/14ab186f-d324-4b6a-b6fd-cb1cf5797eb0/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Multiple merger coalescents: truncated offspring distribu
tions\, large sample sizes\, and bottlenecks - Jonathan Chetwynd-Diggle (U
niversity of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Large deviations of subgraph counts for sparse random graphs - Am
ir Dembo (Stanford University)
DTSTART;VALUE=DATE-TIME:20190603T120000
DTEND;VALUE=DATE-TIME:20190603T130000
UID:https://talks.ox.ac.uk/talks/id/464a7b07-844f-4afb-a4e1-5b10241f9245/
DESCRIPTION:In this talk\, based on a recent joint work with Nick Cook\, I
will discuss recent developments in the emerging theory of nonlinear larg
e deviations focusing on sharp upper tails for counts of a fixed subgraph
in a large sparse Erdos–Renyi graph. In particular\, I will explain our
approach via quantitative versions of the regularity and counting lemmas s
uitable for the study of sparse random graphs in the large deviations regi
me. \nSpeakers:\nAmir Dembo (Stanford University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/464a7b07-844f-4afb-a4e1-5b10241f9245/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Large deviations of subgraph counts for sparse random gra
phs - Amir Dembo (Stanford University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Interacting reflected diffusions and their hydrodynamic limits - C
layton Barnes (Université de Neuchâtel)
DTSTART;VALUE=DATE-TIME:20190617T120000
DTEND;VALUE=DATE-TIME:20190617T130000
UID:https://talks.ox.ac.uk/talks/id/5181ee6a-7b0a-4284-bd9e-3b63e635d3d4/
DESCRIPTION:We introduce recent work studying systems of diffusion that in
teract through their reflection term (local time). We discuss how the hydr
odynamic limit of such systems\, i.e. the large-scale behavior of the empi
rical process\, will converge to a nonlinear PDE whose solution exhibits i
nteraction with the past values at the boundary. If time allows\, we will
discuss aspects of the proofs and how the uniqueness of such PDEs follows
from a stochastic representation.\nSpeakers:\nClayton Barnes (Université
de Neuchâtel)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/5181ee6a-7b0a-4284-bd9e-3b63e635d3d4/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Interacting reflected diffusions and their hydrodynamic l
imits - Clayton Barnes (Université de Neuchâtel)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universal vanishing corrections on the position of fronts in the F
isher-KPP class - Éric Brunet (Laboratoire de Physique Statistique\, ENS
Paris)
DTSTART;VALUE=DATE-TIME:20190429T120000
DTEND;VALUE=DATE-TIME:20190429T130000
UID:https://talks.ox.ac.uk/talks/id/97b4a567-7908-43e9-b2d2-800f032df33d/
DESCRIPTION:The distribution function of the rightmost particle in a branc
hing Brownian \nmotion satisfies the Fisher-KPP equation:\n\n∂u/∂t =
∂²u/∂x² + u - u²\n\nSuch an equation appears also in biology\, chem
istry or theoretical physics\nto describe a moving interface\, or a front\
, between a stable and an unstable \nmedium.\n\nThirty years ago\, Bramson
gave rigorous sharp estimates on the position of \nthe front\, and\, fift
een years ago\, Ebert and van Saarloos heuristically \nidentified universa
l vanishing corrections.\n\nIn this presentation\, I will present a novel
way to study the position of \nsuch a front\, which allows to recover all
the known terms and find some new \nones. We start by studying a front equ
ation where the non-linearity is \nreplaced by a condition at a free bound
ary\, and we show how to extend our \nresults to the actual Fisher-KPP.\nS
peakers:\nÉric Brunet (Laboratoire de Physique Statistique\, ENS Paris)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/97b4a567-7908-43e9-b2d2-800f032df33d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Universal vanishing corrections on the position of fronts
in the Fisher-KPP class - Éric Brunet (Laboratoire de Physique Statistiq
ue\, ENS Paris)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The critical window for random transposition random walk
- Dominic Yeo (University of Oxford)
DTSTART;VALUE=DATE-TIME:20190513T120000
DTEND;VALUE=DATE-TIME:20190513T130000
UID:https://talks.ox.ac.uk/talks/id/6b578653-67d5-464d-862b-cc51f568404d/
DESCRIPTION:The random walk on the permutations of [N] generated by the tr
anspositions was shown by Diaconis and Shahshahani to mix with sharp cutof
f around N log N /2 steps. However\, Schramm showed that the distribution
of the sizes of the largest cycles concentrates (after rescaling) on the P
oisson-Dirichlet distribution PD(0\,1) considerably earlier\, after (1+\\e
psilon)N/2 steps. We show that this behaviour in fact emerges precisely du
ring the critical window of (1+\\lambda N^{-1/3}) N/2 steps\, as \\lambda
\\rightarrow\\infty. Our methods are rather different\, and involve an an
alogy with the classical Erdos-Renyi random graph process\, the metric sca
ling limits of a uniformly-chosen connected graph with a fixed finite numb
er of surplus edges\, and analysing the directed cycle structure of large
3-regular graphs. Joint work with Christina Goldschmidt.\nSpeakers:\nDomin
ic Yeo (University of Oxford)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/6b578653-67d5-464d-862b-cc51f568404d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The critical window for random transposition random walk
- Dominic Yeo (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anchored expansion in supercritical percolation on nonamenable gra
phs - Jonathan Hermon (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20190507T120000
DTEND;VALUE=DATE-TIME:20190507T130000
UID:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
DESCRIPTION:Let G be a transitive nonamenable graph\, and consider supercr
itical Bernoulli bond percolation on G. We prove that the probability that
the origin lies in a finite cluster of size n decays exponentially in n.
We deduce that: \n\n1. Every infinite cluster has anchored expansion almos
t surely. This answers positively a question of Benjamini\, Lyons\, and Sc
hramm (1997). \n\n2. Various observables\, including the percolation proba
bility and the truncated susceptibility are analytic functions of p throug
hout the entire supercritical phase.\n\nJoint work with Tom Hutchcroft. \n
Speakers:\nJonathan Hermon (University of Cambridge)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/1fa9bea7-0fa5-4981-a842-26111ed1dcba/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Anchored expansion in supercritical percolation on noname
nable graphs - Jonathan Hermon (University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:A (2+1)-dimensional Anisotropic KPZ growth model with a smooth pha
se - Sunil Chhita (Durham University)
DTSTART;VALUE=DATE-TIME:20190304T110000Z
DTEND;VALUE=DATE-TIME:20190304T120000Z
UID:https://talks.ox.ac.uk/talks/id/1d0df856-d9fb-4e21-83aa-d3fc889defec/
DESCRIPTION:Stochastic growth processes in dimension (2+1) were conjecture
d by D. Wolf\, on the basis of renormalization-group arguments\, to fall i
nto two distinct universality classes known as the isotropic KPZ class and
the anisotropic KPZ class (AKPZ). The former is characterized by strictly
positive growth and roughness exponents\, while in the AKPZ class\, fluct
uations are logarithmic in time and space. These classes are determined by
the sign of the determinant of the Hessian of the speed of growth.\n\nIt
is natural to ask (a) if one can exhibit interesting growth models with "s
mooth" stationary states\, i.e.\, with O(1) fluctuations (instead of logar
ithmically or power-like growing\, as in Wolf's picture) and (b) what new
phenomena arise when the speed of growth is not smooth\, so that its Hessi
an is not defined. These two questions are actually related and in this ta
lk\, we provide an answer to both\, in a specific framework. This is joint
work with Fabio Toninelli (CNRS and Lyon 1).\nSpeakers:\nSunil Chhita (Du
rham University)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/1d0df856-d9fb-4e21-83aa-d3fc889defec/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:A (2+1)-dimensional Anisotropic KPZ growth model with a s
mooth phase - Sunil Chhita (Durham University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branching Brownian motion with selection and a free boundary probl
em - Sarah Penington (University of Bath)
DTSTART;VALUE=DATE-TIME:20190218T120000Z
DTEND;VALUE=DATE-TIME:20190218T130000Z
UID:https://talks.ox.ac.uk/talks/id/53327d3a-3bbc-459a-8ec0-3090b6d7f814/
DESCRIPTION:Consider a system of N particles moving according to Brownian
motions and branching at rate one. Each time a particle branches\, the par
ticle in the system furthest from the origin is killed. It turns out that
we can use results about a related free boundary problem to control the lo
ng term behaviour of this particle system for large N.\n\nThis is joint wo
rk with Julien Berestycki\, Eric Brunet and James Nolen.\nSpeakers:\nSarah
Penington (University of Bath)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/53327d3a-3bbc-459a-8ec0-3090b6d7f814/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Branching Brownian motion with selection and a free bound
ary problem - Sarah Penington (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Wong-Zakai theorem for stochastic heat equation - Yu Gu (Carne
gie Mellon University)
DTSTART;VALUE=DATE-TIME:20190225T120000Z
DTEND;VALUE=DATE-TIME:20190225T130000Z
UID:https://talks.ox.ac.uk/talks/id/3222b482-cad7-455f-95ed-18a7a631efd2/
DESCRIPTION:We will present a probabilistic proof of the Wong-Zakai theore
m for stochastic heat equation by Hairer-Pardoux.\nSpeakers:\nYu Gu (Carne
gie Mellon University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3222b482-cad7-455f-95ed-18a7a631efd2/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The Wong-Zakai theorem for stochastic heat equation - Yu
Gu (Carnegie Mellon University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:U-statistics: some old and new results with applications to patter
ns in random strings and permutations - Svante Janson (Uppsala University)
DTSTART;VALUE=DATE-TIME:20190211T120000Z
DTEND;VALUE=DATE-TIME:20190211T130000Z
UID:https://talks.ox.ac.uk/talks/id/b9bbf382-7e7c-4f21-9642-b9f5c70e3ce8/
DESCRIPTION:U-statistics form a large class of random variables that appea
r in many contexts. I will focus on some simple and some less obvious appl
ications to patterns in random permutations and random strings\, and gener
al results useful in these applications (and sometimes motivated by them).
This will include some less common versions of U-statistics (asymmetric U
-statistics and U-statistics based on an m-dependent sequence)\, and some
new results on renewal theory for U-statistics.\nSpeakers:\nSvante Janson
(Uppsala University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b9bbf382-7e7c-4f21-9642-b9f5c70e3ce8/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:U-statistics: some old and new results with applications
to patterns in random strings and permutations - Svante Janson (Uppsala Un
iversity)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Infinitely ramified point measure and branching Lévy process - Ba
stien Mallein (Paris 13)
DTSTART;VALUE=DATE-TIME:20190128T120000Z
DTEND;VALUE=DATE-TIME:20190128T130000Z
UID:https://talks.ox.ac.uk/talks/id/e7aeb00f-87c1-41cd-ad2c-17605c7afe44/
DESCRIPTION:An infinitely ramified point measure is a random point measure
that can be written as the terminal value of a branching random walk of a
ny length. This is the equivalent\, in branching processes theory\, to the
notion of infinitely divisible random variables for real-valued random va
riables. In this talk\, we show a connexion between infinitely ramified po
int measures and branching Lévy processes\, a continuous-time particle sy
stem on the real line\, in which particles move according to independent L
évy processes\, and give birth to children in a Poisson fashion.\n\nSpeak
ers:\nBastien Mallein (Paris 13)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e7aeb00f-87c1-41cd-ad2c-17605c7afe44/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Infinitely ramified point measure and branching Lévy pro
cess - Bastien Mallein (Paris 13)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orderings of Gibbs random samples - Yuri Yakubovich (St Petersburg
State University)
DTSTART;VALUE=DATE-TIME:20190121T120000Z
DTEND;VALUE=DATE-TIME:20190121T130000Z
UID:https://talks.ox.ac.uk/talks/id/3caadf9c-f9b7-43b3-9f75-18c738f6423e/
DESCRIPTION:Random partitions of finite sets play a key role in modelling
genetic diversity. The basic problem is to draw statistical inference abo
ut the general population where a sample partition on species is only obse
rvable. Mathematical models are greatly simplified by assuming that the po
pulation itself is a sample from an idealized infinite population\, due to
Kingman’s theory of exchangeable random partitions of countable sets\,
whereby partitions are modelled by sampling from a random discrete distrib
ution. In population genetics\, the sample values may carry additional cha
racteristics of the species. For example\, in Moran’s model with infinit
ely many alleles\, such a characteristic encodes the relative age of speci
es\, and the question of interest is\, given the observed frequencies of s
pecies in the sample\, to order them by age. Donnelly & Tavaré (1986) pro
ved that in the GEM(θ) model (which leads to the famous Ewens sampling fo
rmula)\, the distribution of the order by age is the same as that of the o
rder by appearance. In my talk\, I will show that in a two-parametric gene
ralization of the GEM model\, and more generally\, under the so-called Gib
bs sampling\, these two orders have different distributions which are neve
rtheless connected via a modification of the stochastic procedure known as
size-biased ordering.\nThis is joint work with Jim Pitman (Berkeley)\, do
i:10.1214/17-EJP59\; doi:10.1214/17-ECP95.\nSpeakers:\nYuri Yakubovich (St
Petersburg State University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/3caadf9c-f9b7-43b3-9f75-18c738f6423e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Orderings of Gibbs random samples - Yuri Yakubovich (St P
etersburg State University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Particle systems and systemic risk - Ben Hambly (University of Oxf
ord)
DTSTART;VALUE=DATE-TIME:20190114T120000Z
DTEND;VALUE=DATE-TIME:20190114T130000Z
UID:https://talks.ox.ac.uk/talks/id/925fb523-8dcd-4aae-871e-d325a1dccd82/
DESCRIPTION:Systemic risk in the banking system is the risk that small los
ses and defaults can escalate through endogenous effects to cause an event
affecting large parts of the financial sector. We will consider some simp
le particle system models for the interactions between banks and show how
this leads to stochastic McKean-Vlasov equations describing the whole syst
em. The systemic risk can be captured through a loss function and we will
show that this can have unexpected behaviour in different models.\nSpeaker
s:\nBen Hambly (University of Oxford)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/925fb523-8dcd-4aae-871e-d325a1dccd82/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Particle systems and systemic risk - Ben Hambly (Universi
ty of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Metastable behaviour of the dilute Curie-Weiss model - Martin Slow
ik (TU Berlin)
DTSTART;VALUE=DATE-TIME:20181126T120000Z
DTEND;VALUE=DATE-TIME:20181126T130000Z
UID:https://talks.ox.ac.uk/talks/id/d9912ad8-b9b5-4123-a72d-d6a53ad4903b/
DESCRIPTION:Metastability is a phenomenon that occurs in the dynamics of a
multi-stable non-linear system subject to noise. It is characterized by
the existence of multiple\, well separated time scales. The talk will be
focus on the metastable behavior of the dilute Curie-Weiss model\, that is
a Ising spin system on a Erdos-Renyi random graph with $N$ vertices and r
etention probability $p \\in (0\,1)$. Each spin interacts with a external
field\, while the interaction among neighbouring spin variables is assumed
to be of the same strength. In particular\, I will discuss bounds on the
mean exit time from the metastable to the stable state and the spectral g
ap.\n\n \nSpeakers:\nMartin Slowik (TU Berlin)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d9912ad8-b9b5-4123-a72d-d6a53ad4903b/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Metastable behaviour of the dilute Curie-Weiss model - Ma
rtin Slowik (TU Berlin)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polynomial mixing time for edge flips on quadrangulations - Alessa
ndra Caraceni (University of Bath)
DTSTART;VALUE=DATE-TIME:20181119T120000Z
DTEND;VALUE=DATE-TIME:20181119T130000Z
UID:https://talks.ox.ac.uk/talks/id/46c81587-5db3-4968-9702-2e7f69e098b7/
DESCRIPTION:This talk will revolve around recent joint work with Alexandre
Stauffer in which we give the first polynomial upper bound for the relaxa
tion time of the edge flip Markov chain on rooted quadrangulations. A quad
rangulation of size n is a connected planar graph endowed with a cellular
embedding in the sphere such that all of its n faces have degree 4\, consi
dered up to orientation-preserving homeomorphisms of the sphere itself\; w
e call it rooted when it is endowed with a distinguished oriented edge. Gi
ven a (rooted) quadrangulation of size n\, a step of the Markov chain we a
re interested in – a so-called “edge flip” – consists in choosing
an edge uniformly at random\, deleting it and replacing it with one of the
three possible edges (two when the original edge is adjacent to only one
face) which\, if drawn\, recreate a quadrangulation. We will see how one c
an relate the edge flip chain on quadrangulations to a “leaf translation
” chain on plane trees (which has a natural interpretation as a chain on
the set of Dyck paths\, and on other Catalan structures as well). Having
discussed how to set up a successful comparison between the two chains whi
ch exploits the well-known bijection by Schaeffer and a specific construct
ion of leaf translations as sequences of edge flips\, we shall estimate th
e relaxation time of the leaf translation chain\, thereby improving on a r
esult by Movassagh and Shor.\nSpeakers:\nAlessandra Caraceni (University o
f Bath)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/46c81587-5db3-4968-9702-2e7f69e098b7/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Polynomial mixing time for edge flips on quadrangulations
- Alessandra Caraceni (University of Bath)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algorithmic Pirogov-Sinai Theory - Tyler Helmuth (University of Br
istol)
DTSTART;VALUE=DATE-TIME:20181112T120000Z
DTEND;VALUE=DATE-TIME:20181112T130000Z
UID:https://talks.ox.ac.uk/talks/id/8558c060-74a2-4acd-a1de-9407263e6492/
DESCRIPTION:The hard-core model is a basic and important model in statisti
cal mechanics\, probability\, and theoretical computer science. I’ll int
roduce the model\, and after describing some known algorithmic results\, w
ill discuss a polynomial-time algorithm for approximately sampling from th
e hard-core model at high densities on the integer lattices. This is the r
egime in which the Glauber dynamics are known to mix exponentially slowly.
Our algorithm relies in an essential way on Pirogov-Sinai theory\, an imp
ortant tool for understanding the phase diagram of high-density discrete s
tatistical mechanics models. \n\nThis is joint work with Will Perkins and
Guus Regts.\nSpeakers:\nTyler Helmuth (University of Bristol)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/8558c060-74a2-4acd-a1de-9407263e6492/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Algorithmic Pirogov-Sinai Theory - Tyler Helmuth (Univers
ity of Bristol)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Branching Brownian motion with decay of mass and the non-local Fis
her-KPP equation - Julien Berestycki (University of Oxford)
DTSTART;VALUE=DATE-TIME:20181105T120000Z
DTEND;VALUE=DATE-TIME:20181105T130000Z
UID:https://talks.ox.ac.uk/talks/id/9ffb5852-ff86-4773-842d-d7849d33538e/
DESCRIPTION:The non-local variant of the celebrated Fisher-KPP equation de
scribes the growth and spread of population in which individuals diffuse\,
reproduce and - crucially - interact through a non-local competition mech
anism. This type of equation is intrinsically harder to study than the cla
ssical Fisher-KPP equation because we lose such powerful tools as the comp
arison principle and the maximum principle. In this talk\, I will show how
this equation arises as the hydrodynamic limit of a particle system -the
branching Brownian motion with decay of mass\, and use this to study front
propagation behaviours.\n\nThis is based on joint work with Louigi Addari
o-Berry and Sarah Penington.\nSpeakers:\nJulien Berestycki (University of
Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/9ffb5852-ff86-4773-842d-d7849d33538e/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Branching Brownian motion with decay of mass and the non-
local Fisher-KPP equation - Julien Berestycki (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finding cliques using few probes - Miklós Rácz (Princeton Unive
rsity)
DTSTART;VALUE=DATE-TIME:20181029T120000Z
DTEND;VALUE=DATE-TIME:20181029T130000Z
UID:https://talks.ox.ac.uk/talks/id/e96d4efd-c944-4dd3-8684-25f1eba6b948/
DESCRIPTION:I will talk about algorithms (with unlimited computational pow
er) which adaptively probe pairs of vertices of a graph to learn the prese
nce or absence of edges and whose goal is to output a large clique. I will
focus on the case of the random graph G(n\,1/2)\, in which case the size
of the largest clique is roughly 2\\log(n). Our main result shows that if
the number of pairs queried is linear in n and adaptivity is restricted to
finitely many rounds\, then the largest clique cannot be found\; more pre
cisely\, no algorithm can find a clique larger than c\\log(n) where c < 2
is an explicit constant. This is joint work with Uriel Feige\, David Gamar
nik\, Joe Neeman\, and Prasad Tetali. \nSpeakers:\nMiklós Rácz (Princeto
n University)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e96d4efd-c944-4dd3-8684-25f1eba6b948/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Finding cliques using few probes - Miklós Rácz (Prince
ton University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamics of limit order books: queueing models\, diffusion limits
and stochastic PDEs - Rama Cont (University of Oxford)
DTSTART;VALUE=DATE-TIME:20181015T120000
DTEND;VALUE=DATE-TIME:20181015T130000
UID:https://talks.ox.ac.uk/talks/id/d1074e46-233c-45a6-a47d-8a1b2db1de15/
DESCRIPTION:The advent of electronic trading in financial markets has led
to a market landscape in which buyers and sellers by submitting orders thr
ough a central limit order book\, where orders are matched and executed a
ccording to time and price priority. The wide range of frequencies involve
d - from microseconds to days - requires a consistent description of mark
et dynamics across time scales.\n\nBased on a detailed empirical study of
high frequency order flow in equity and futures markets\, we propose a mul
ti-scale stochastic model for dynamics of price and order flow in a limit
order market\, which captures the coexistence of high frequency and low fr
equency order flow and examines the consequences of this heterogeneity on
intraday price dynamics\, volatility and liquidity.\n\nWe then use probabi
listic limit theorems to derive the dynamics of the order book and market
price at various time scales. \nStarting from a description of the order b
ook as a multi-class spatial queueing system at the highest (micro- or mi
lli-second) frequency\, we show that over intermediate time scales -- sec
onds -- the dynamics of the active queues may be described as a diffusion
in a wedge with discontinuous reflection at the boundary\, while the marke
t price follows a jump process driven by the boundary local time of this d
iffusion.\n\nOver longer time scales\, the effective dynamics of the order
book may be described as a stochastic moving boundary problem while the
market price follows a diffusion in a random environment defined by the or
der book. We will emphasise how asymptotics across time scales provides in
sights into the relations between supply\, demand\, liquidity and volatili
ty in limit order markets.\nSpeakers:\nRama Cont (University of Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/d1074e46-233c-45a6-a47d-8a1b2db1de15/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Dynamics of limit order books: queueing models\, diffusi
on limits and stochastic PDEs - Rama Cont (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Where do second class particles walk? - Márton Balázs (Universit
y of Bristol)
DTSTART;VALUE=DATE-TIME:20181022T120000
DTEND;VALUE=DATE-TIME:20181022T130000
UID:https://talks.ox.ac.uk/talks/id/e7dc4443-a2dd-4dbf-867d-c910db5ad4b5/
DESCRIPTION:I will tell about a long story in interacting particle systems
that emerged across decades in several stages:\n\n1. A second class parti
cle in asymmetric exclusion (ASEP) and in an exponential bricklayers proce
ss (EBPL) sees certain shock-like distributions stationary.\n\n2. Such sho
ck-like distributions perform a simple random walk in both ASEP and EBLP (
what does that mean...?)\n\n3. It is in fact the second class particle in
the middle of the shock that does the random walk (what does THIS mean...?
). Besides ASEP and EBLP\, it also works for an exponential zero range pro
cess (EZRP).\n\n4. Q-zero range is yet another example that has this rando
m walking property. The second class particle really helps to reveal this
secret here.\n\nThe last step is recent\, the ones before are old results.
\n\n(Joint work with Gyorgy Farkas\, Peter Kovacs\, Attila Rakos\; Lewis D
uffy\, Dimitri Pantelli)\nSpeakers:\nMárton Balázs (University of Bristo
l)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e7dc4443-a2dd-4dbf-867d-c910db5ad4b5/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Where do second class particles walk? - Márton Balázs (
University of Bristol)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limits of (randomly) growing Schröder trees and exchangeability -
Julian Gerstenberg (Leibniz Universität Hannover)
DTSTART;VALUE=DATE-TIME:20181008T120000
DTEND;VALUE=DATE-TIME:20181008T130000
UID:https://talks.ox.ac.uk/talks/id/16131e1b-de82-4227-ad4a-ab46c536a9a0/
DESCRIPTION:We consider finite rooted ordered trees in which every interna
l node has at least two children\, sometimes called Schröder trees\; the
size |t| of such a tree t is the number of its leaves. An important concep
t with trees is that of inducing subtrees. Given a tree t of size k and a
larger tree t' of size n\\geq k we define 0 \\leq \\theta(t\,t')\\leq 1 to
be the probability of obtaining t as a randomly induced subtree of size k
in t'. One can think of \\theta(t\,t') to be the _density of the pattern
t in t'_. In this talk we consider two closely related questions concernin
g the nature of \\theta:\n1. A sequences of trees (t_n)_n with |t_n|\\righ
tarrow\\infty is called \\theta-convergent\, if \\theta(t\,t_n) converges
for every fixed tree t. The limit of (t_n)_n is the function t\\mapsto \\l
im_n\\theta(t\,t_n). What limits exist? \n2. A Markov chain (X_n)_n with X
_n being a random tree of size n is called a \\theta-chain if P(X_k=t|X_n=
t')=\\theta(t\,t') for all k \\leq n. What \\theta-chains exist?\n\nSimila
r questions have been treated for many different types of discrete structu
res (words\, permutations\, graphs \\dots)\; binary Schröder trees (Catal
an trees) are considered in [1]. We present a De Finetti-type representati
on for \\theta-chains and a homeomorphic description of limits of \\theta-
convergent sequences involving certain tree-like compact subsets of the sq
uare [0\,1]^2. Questions and results are closely linked to the study of ex
changeable hierarchies\, see [2]. \n\n[1] Evans\, Grübel and Wakolbinger.
"Doob-Martin boundary of Rémy's tree growth chain". The Annals of Probab
ility\, 2017.\n[2] Forman\, Haulk and Pitman. "A representation of exchang
eable hierarchies by sampling from random real trees". Prob.Theory and rel
ated Fields\, 2017.\n[3] Gerstenberg. "Exchangeable interval hypergraphs a
nd limits of ordered discrete structures". arXiv\, 2018.\nSpeakers:\nJulia
n Gerstenberg (Leibniz Universität Hannover)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/16131e1b-de82-4227-ad4a-ab46c536a9a0/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Limits of (randomly) growing Schröder trees and exchange
ability - Julian Gerstenberg (Leibniz Universität Hannover)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuous-state branching process with dependent immigration - Ze
nghu Li (Beijing Normal University)
DTSTART;VALUE=DATE-TIME:20180606T120000
DTEND;VALUE=DATE-TIME:20180606T130000
UID:https://talks.ox.ac.uk/talks/id/bb91ed75-e520-4ac7-8099-ab1e76c74173/
DESCRIPTION:We are interested in a population model called continuous-stat
e branching process with dependent immigration (CBDI-processes). The immig
ration rate of the model depends on the current population size via a func
tion that can be non-Lipschitz. We give a construction of the process usin
g a stochastic equation driven by Poisson point measures on some path spac
es. This approach gives a direct construction of the sample path of the pr
ocess with general branching and immigration mechanisms from those of the
corresponding CB-process without immigration. By choosing the ingredients
suitably\, we can get either a new CB-process with different branching mec
hanism or a branching model with competition. We focus on the one-dimensio
nal model\, but the arguments carry over to the measure-valued setting. Th
ese kinds of constructions have been proved useful for the study of some f
inancial problems.\nSpeakers:\nZenghu Li (Beijing Normal University)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/bb91ed75-e520-4ac7-8099-ab1e76c74173/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Continuous-state branching process with dependent immigra
tion - Zenghu Li (Beijing Normal University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mermin-Wagner Theorem for vertex-reinforced jump process - Roland
Bauerschmidt (Statslab\, University of Cambridge)
DTSTART;VALUE=DATE-TIME:20180604T120000
DTEND;VALUE=DATE-TIME:20180604T130000
UID:https://talks.ox.ac.uk/talks/id/2a0f9713-38ff-46ea-ab08-0de595401bbf/
DESCRIPTION:The vertex-reinforced jump process (VJRP) is a random walk tha
t prefers to jump to vertices visited in the past. Hyperbolic sigma models
are\nspin models where the spins take values in a hyperbolic space. I wil
l explain a relation between the VRJP and hyperbolic sigma models which\np
arallels that between the simple random walk and the Gaussian free field.
I will further show a Mermin-Wagner Theorem for hyperbolic sigma\nmodels w
hich implies that the VRJP is recurrent in two dimensions.\n\nThis is join
t work with Tyler Helmuth and Andrew Swan.\nSpeakers:\nRoland Bauerschmidt
(Statslab\, University of Cambridge)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/2a0f9713-38ff-46ea-ab08-0de595401bbf/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Mermin-Wagner Theorem for vertex-reinforced jump process
- Roland Bauerschmidt (Statslab\, University of Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limiting directions for random walks in affine Weyl groups - Arvin
d Ayyer (Indian Institute of Science\, Bangalore)
DTSTART;VALUE=DATE-TIME:20180521T120000
DTEND;VALUE=DATE-TIME:20180521T130000
UID:https://talks.ox.ac.uk/talks/id/16725332-6d01-4154-8d50-cce4c902cbf9/
DESCRIPTION:The multispecies totally asymmetric simple exclusion process (
MTASEP) is an interacting particle system defined on a finite one-dimensio
nal integer lattice with periodic boundary conditions. The exact stationar
y distribution of this Markov process was described by P. Ferrari and J. M
artin using multiclass M/M/1 queues. Recently\, T. Lam considered a random
walk on the alcoves of an affine Weyl group conditioned never to cross th
e same hyperplane twice. He proved that the limiting direction of this wal
k exists almost surely\, and conjectured a formula for it for \\tilde{A}_n
. I will describe joint work with S. Linusson\, where we solved this conje
cture by computing this limiting direction as certain correlations of the
MTASEP.\n\nTime permitting\, I will describe extensions of our work for th
e affine Weyl group \\tilde{C}_n. This involves the study of correlations
in a multispecies exclusion process with open boundaries (i.e.\, allowing
the entry and exit of particles). Here\, we have also computed this limiti
ng direction building on existing work of C. Arita\, in joint work with E.
Aas\, S. Linusson and S. Potka.\nSpeakers:\nArvind Ayyer (Indian Institut
e of Science\, Bangalore)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/16725332-6d01-4154-8d50-cce4c902cbf9/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Limiting directions for random walks in affine Weyl group
s - Arvind Ayyer (Indian Institute of Science\, Bangalore)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Four-dimensional loop-erased random walk and uniform spanning tree
- Wei Wu (Department of Statistics\, University of Warwick)
DTSTART;VALUE=DATE-TIME:20180514T120000
DTEND;VALUE=DATE-TIME:20180514T130000
UID:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
DESCRIPTION:Critical lattice models are believed to converge to a free fie
ld in the scaling limit\, at or above their critical dimension. This has b
een established for Ising and \\Phi^4 models for d \\geq 4. We describe a
simple spin model from uniform spanning forests in Z^d whose critical dime
nsion is 4 and prove that the scaling limit is the bi-Laplacian Gaussian f
ield for d\\geq 4. At dimension 4\, there is a logarithmic correction for
the spin-spin correlation and the bi-Laplacian Gaussian field is a log cor
related field. The proof also improves the known mean field picture of LER
W in d=4: we show that the renormalized escape probability (and arm events
) of 4D LERW converge to some "continuum escaping probability". Based on j
oint works with Greg Lawler and Xin Sun. \n\nSpeakers:\nWei Wu (Department
of Statistics\, University of Warwick)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/b5d9bccd-240a-4cc9-bd84-c0624b627b7f/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Four-dimensional loop-erased random walk and uniform span
ning tree - Wei Wu (Department of Statistics\, University of Warwick)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:High-density hard-core configurations on a triangular lattice - Yu
ri Suhov (Penn State and Cambridge)
DTSTART;VALUE=DATE-TIME:20180601T120000
DTEND;VALUE=DATE-TIME:20180601T130000
UID:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
DESCRIPTION:The high-density hard-core configuration model has attracted a
ttention for quite a long time. The first rigorous results about the phase
transition on a lattice with a nearest-neighbor exclusion where published
by Dobrushin in 1968. In 1979\, Baxter calculated the free energy and spe
cified the critical point on a triangular lattice with a nearest-neighbor
exclusion\; in 1980 Andrews gave a rigorous proof of Baxter's calculation
with the help of Ramanujan's identities. On a square lattice the nearest-n
eighbor exclusion critical point has been estimated from above and below i
n a series by a number of authors.\n\nWe analyze the hard-core model on a
triangular lattice and identify the extreme Gibbs measures (pure phases) f
or high densities. Depending on arithmetic properties of the hard-core dia
meter $D$\, the number of pure phases equals either $D^2$ or $2D^2$. A cla
ssification of possible cases can be given in terms of Eisenstein primes.\
n\nIf the time allows\, I will mention 3D analogs of some of these results
.\n\nThis is a joint work with A Mazel and I Stuhl\; cf. arXiv:1803.04041.
No special knowledge will be assumed from the audience.\n\n\nSpeakers:\nY
uri Suhov (Penn State and Cambridge)
LOCATION:Mathematical Institute (L5)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
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ACTION:display
DESCRIPTION:Talk:High-density hard-core configurations on a triangular lat
tice - Yuri Suhov (Penn State and Cambridge)
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SUMMARY:Mallows permutations and stable marriage - Alexander Holroyd
DTSTART;VALUE=DATE-TIME:20180509T120000
DTEND;VALUE=DATE-TIME:20180509T130000
UID:https://talks.ox.ac.uk/talks/id/e9ff1f21-9776-4fcf-8e15-fa35f3c5f125/
DESCRIPTION:The Mallows measure on the symmetric group S_n assigns to each
permutation a probability proportional to a parameter q to the power of t
he inversion number. It was originally introduced in 1957 in the context o
f statistical ranking theory\, and has been used in many areas including s
tatistical physics\, learning theory\, mixing times\, and finite dependenc
e. Gale-Shapley stable marriage is a cornerstone of economic theory as wel
l a mathematical gem. Introduced in 1962\, it was the subject of the 2012
Nobel prize in economics\, awarded to Roth and Shapley. I'll explain how t
he two objects are related. In particular\, the former is an example of th
e latter. Among other things this gives a simple and elegant new descripti
on of the Mallows measure on the infinite line Z\, provided one does not g
et distracted by "wild matchings"!\nSpeakers:\nAlexander Holroyd
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/e9ff1f21-9776-4fcf-8e15-fa35f3c5f125/
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DESCRIPTION:Talk:Mallows permutations and stable marriage - Alexander Holr
oyd
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BEGIN:VEVENT
SUMMARY:On the number of arithmetic progressions in sparse random sets - C
hristoph Koch (Department of Statistics\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20180423T120000
DTEND;VALUE=DATE-TIME:20180423T130000
UID:https://talks.ox.ac.uk/talks/id/50cd5e62-d126-4531-a276-f7ed5417f890/
DESCRIPTION:We study arithmetic progressions $\\{a\,a+b\,a+2b\,\\dots\,a+(
\\ell-1) b\\}$\, with $\\ell\\ge 3$\, in random subsets of the initial seg
ment of natural numbers $[n]:=\\{1\,2\,\\dots\, n\\}$. Given $p\\in[0\,1]$
we denote by $[n]_p$ the random subset of $[n]$ which includes every numb
er with probability $p$\, independently of one another. The focus lies on
sparse random subsets\, i.e.\\ when $p=p(n)=o(1)$ with respect to $n\\to\\
infty$.\n\nLet $X_\\ell$ denote the number of distinct arithmetic progress
ions of length $\\ell$ which are contained in $[n]_p$. We determine the li
miting distribution for $X_\\ell$ not only for fixed $\\ell\\ge 3$ but als
o when $\\ell=\\ell(n)\\to\\infty$ sufficiently slowly. Moreover\, we pro
ve a central limit theorem for the joint distribution of the pair $(X_{\\e
ll}\,X_{\\ell'})$ for a wide range of $p$. Our proofs are based on the met
hod of moments and combinatorial arguments\, such as an algorithmic enumer
ation of collections of arithmetic progressions.\n\nThis is joint work wit
h Yacine Barhoumi-Andr\\'eani and Hong Liu (University of Warwick).\nSpeak
ers:\nChristoph Koch (Department of Statistics\, University of Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/50cd5e62-d126-4531-a276-f7ed5417f890/
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DESCRIPTION:Talk:On the number of arithmetic progressions in sparse random
sets - Christoph Koch (Department of Statistics\, University of Oxford)
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BEGIN:VEVENT
SUMMARY:Max-Average Games with Random Payoffs - Rahul Santhanam (Departmen
t of Computer Science\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20180430T120000
DTEND;VALUE=DATE-TIME:20180430T130000
UID:https://talks.ox.ac.uk/talks/id/2c8a4425-8850-49f9-b3d4-33d4d5e92550/
DESCRIPTION:Consider the following simple 2-person sequential game with i.
i.d. payoffs. The 2 players\, Max and Average\, each have exactly 2 option
s for each\nmove. Max plays optimally\, i.e.\, to maximize her payoff\, an
d Average plays randomly. How does the expected payoff for Max depend on t
he distribution on payoffs?\n\nI will describe the complexity-theoretic mo
tivation for this question\, and describe some preliminary results when th
e distribution on payoffs is Bernoulli.\n\nJoint work with Andy Drucker.\n
Speakers:\nRahul Santhanam (Department of Computer Science\, University of
Oxford)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/2c8a4425-8850-49f9-b3d4-33d4d5e92550/
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ACTION:display
DESCRIPTION:Talk:Max-Average Games with Random Payoffs - Rahul Santhanam (
Department of Computer Science\, University of Oxford)
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