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BEGIN:VEVENT
SUMMARY:Near-critical percolation with heavy-tailed impurities - Pierre No
lin (City University of Hong Kong)
DTSTART;VALUE=DATE-TIME:20190624T110000Z
DTEND;VALUE=DATE-TIME:20190624T120000Z
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
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:20190624T130000Z
DTEND;VALUE=DATE-TIME:20190624T140000Z
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
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:20190610T110000Z
DTEND;VALUE=DATE-TIME:20190610T120000Z
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
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:20190528T110000Z
DTEND;VALUE=DATE-TIME:20190528T120000Z
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
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:20190520T110000Z
DTEND;VALUE=DATE-TIME:20190520T120000Z
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
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:20190603T110000Z
DTEND;VALUE=DATE-TIME:20190603T120000Z
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
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:20190617T110000Z
DTEND;VALUE=DATE-TIME:20190617T120000Z
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
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:20190429T110000Z
DTEND;VALUE=DATE-TIME:20190429T120000Z
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
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:20190513T110000Z
DTEND;VALUE=DATE-TIME:20190513T120000Z
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
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:20190507T110000Z
DTEND;VALUE=DATE-TIME:20190507T120000Z
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
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
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
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
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
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
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
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
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
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
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
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
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
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:20181015T110000Z
DTEND;VALUE=DATE-TIME:20181015T120000Z
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
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:20181022T110000Z
DTEND;VALUE=DATE-TIME:20181022T120000Z
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
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:20181008T110000Z
DTEND;VALUE=DATE-TIME:20181008T120000Z
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
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:20180606T110000Z
DTEND;VALUE=DATE-TIME:20180606T120000Z
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
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:20180604T110000Z
DTEND;VALUE=DATE-TIME:20180604T120000Z
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
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:20180521T110000Z
DTEND;VALUE=DATE-TIME:20180521T120000Z
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
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:20180514T110000Z
DTEND;VALUE=DATE-TIME:20180514T120000Z
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
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:20180601T110000Z
DTEND;VALUE=DATE-TIME:20180601T120000Z
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
URL:https://talks.ox.ac.uk/talks/id/cc4421bb-ce1a-4a53-9228-b281e6eb7224/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:High-density hard-core configurations on a triangular lat
tice - Yuri Suhov (Penn State and Cambridge)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mallows permutations and stable marriage - Alexander Holroyd
DTSTART;VALUE=DATE-TIME:20180509T110000Z
DTEND;VALUE=DATE-TIME:20180509T120000Z
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
URL:https://talks.ox.ac.uk/talks/id/e9ff1f21-9776-4fcf-8e15-fa35f3c5f125/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Mallows permutations and stable marriage - Alexander Holr
oyd
TRIGGER:-PT1H
END:VALARM
END:VEVENT
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:20180423T110000Z
DTEND;VALUE=DATE-TIME:20180423T120000Z
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
URL:https://talks.ox.ac.uk/talks/id/50cd5e62-d126-4531-a276-f7ed5417f890/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:On the number of arithmetic progressions in sparse random
sets - Christoph Koch (Department of Statistics\, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max-Average Games with Random Payoffs - Rahul Santhanam (Departmen
t of Computer Science\, University of Oxford)
DTSTART;VALUE=DATE-TIME:20180430T110000Z
DTEND;VALUE=DATE-TIME:20180430T120000Z
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
URL:https://talks.ox.ac.uk/talks/id/2c8a4425-8850-49f9-b3d4-33d4d5e92550/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Max-Average Games with Random Payoffs - Rahul Santhanam (
Department of Computer Science\, University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
END:VCALENDAR