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SUMMARY:Scattered thoughts from applied probability: networks\, security
queues and prediction tournaments - Prof David Aldous (University of Calif
ornia\, Berkeley)
DTSTART;VALUE=DATE-TIME:20190614T143000Z
DTEND;VALUE=DATE-TIME:20190614T153000Z
UID:https://talks.ox.ac.uk/talks/id/ccd94884-102e-473b-add9-4ca68e84bffa/
DESCRIPTION:A sample of topics that have caught my eye in recent years.\n\
n(a) Prediction tournaments are like sports in that a higher-ranked player
will likely score better than a lower-ranked one. But paradoxically\, un
der a reasonable model the winner of a tournament is relatively less likel
y to be a top-ranked player\, maybe clouding the interpretation of multimi
llion dollar IARPA-sponsored projects.\n\n(b) At the back of a long queue
at airport security\, you stand still until a wave of motion reaches you\;
a non-standard model gives quantitative predictions for such waves.\n\n(
c) Spatial networks give rise to intriguing questions. For instance\, sup
pose (as a bizarre fantasy) that an eccentric multi-billionaire proposes t
o solve traffic congestion in a huge metropolitan region by digging underg
round tunnels through which cars can move very fast\; where to dig the tun
nels?\n\n(d) As a hard technical question\, epidemic models combine a mode
l for a contact network with a model for transmission between contacts\, w
ith various parameters including an infectiousness parameter $\\rho$. Int
uitively\, there is always a critical value $\\rho_c$ such that\, starting
with a sprinkling of $o(n)$ infectives\, there will w.h.p. be a pandemic
if $\\rho > \\rho_c$ but w\,h\,p. not if $\\rho < \\rho_c$. This is true
in familiar specific models for the contact network\, but can we prove thi
s for all contact networks?\n\nSpeakers:\nProf David Aldous (University of
California\, Berkeley)
LOCATION:24-29 St Giles' (Large Lecture Theatre (LG.01))\, 24-29 St Giles'
OX1 3LB
URL:https://talks.ox.ac.uk/talks/id/ccd94884-102e-473b-add9-4ca68e84bffa/
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ACTION:display
DESCRIPTION:Talk:Scattered thoughts from applied probability: networks\,
security queues and prediction tournaments - Prof David Aldous (University
of California\, Berkeley)
TRIGGER:-PT1H
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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/
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ACTION:display
DESCRIPTION:Talk:Polynomial mixing time for edge flips on quadrangulations
- Alessandra Caraceni (University of Bath)
TRIGGER:-PT1H
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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/
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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
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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/
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ACTION:display
DESCRIPTION:Talk:Where do second class particles walk? - Márton Balázs (
University of Bristol)
TRIGGER:-PT1H
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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/
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ACTION:display
DESCRIPTION:Talk:Dynamics of limit order books: queueing models\, diffusi
on limits and stochastic PDEs - Rama Cont (University of Oxford)
TRIGGER:-PT1H
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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/
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ACTION:display
DESCRIPTION:Talk:Metastable behaviour of the dilute Curie-Weiss model - Ma
rtin Slowik (TU Berlin)
TRIGGER:-PT1H
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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/
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ACTION:display
DESCRIPTION:Talk:Algorithmic Pirogov-Sinai Theory - Tyler Helmuth (Univers
ity of Bristol)
TRIGGER:-PT1H
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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/
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ACTION:display
DESCRIPTION:Talk:Finding cliques using few probes - Miklós Rácz (Prince
ton University)
TRIGGER:-PT1H
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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
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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/
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ACTION:display
DESCRIPTION:Talk:High-density hard-core configurations on a triangular lat
tice - Yuri Suhov (Penn State and Cambridge)
TRIGGER:-PT1H
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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: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/
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ACTION:display
DESCRIPTION:Talk:On the number of arithmetic progressions in sparse random
sets - Christoph Koch (Department of Statistics\, University of Oxford)
TRIGGER:-PT1H
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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
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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
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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/
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DESCRIPTION:Talk:Mallows permutations and stable marriage - Alexander Holr
oyd
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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/
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DESCRIPTION:Talk:Max-Average Games with Random Payoffs - Rahul Santhanam (
Department of Computer Science\, University of Oxford)
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SUMMARY:Algorithms and Algorithmic Obstacles in High-Dimensional Regressio
n - David Gamarnik (MIT Sloan School of Management\, USA)
DTSTART;VALUE=DATE-TIME:20180427T143000Z
DTEND;VALUE=DATE-TIME:20180427T153000Z
UID:https://talks.ox.ac.uk/talks/id/cf2bfe86-9395-49d1-a6bc-e8ee10e644be/
DESCRIPTION:Many optimization problems arising in studying of random struc
tures exhibit an apparent gap between the optimal values which can be esti
mated by non-constructive means\, and the best values achievable by fast (
polynomial time) algorithms. Through a combined effort of mathematicians\,
computer scientists and statistical physicists\, it became apparent that
a potential and in some cases a provable obstruction for designing algorit
hms bridging this gap is a phase transition in the geometry of nearly opti
mal solutions\, in particular the presence of a certain Overlap Gap Proper
ty (OGP).\n\nIn this talk we discuss this property in the context of spars
e high dimensional linear regression problem with Gaussian design. We show
that\, on the one hand\, in the sampling regime where the known fast meth
ods for this problem are effective\, the space of solutions exhibits a mon
otonicity with respect to the proximity to the ground truth regression vec
tor and no local optimums exist apart from the ground truth. On the other
hand\, once the sampling number is asymptotically in the regime where the
known methods fail\, we show that the monotonicity is lost\, and the model
exhibits an OGP. In the context of the regression problem this means ever
y solution exhibiting a small mean squared error is either fairly close to
the ground truth or is very far from it\, with no middle ground.\nSpeaker
s:\nDavid Gamarnik (MIT Sloan School of Management\, USA)
LOCATION:Large Lecture Theatre
URL:https://talks.ox.ac.uk/talks/id/cf2bfe86-9395-49d1-a6bc-e8ee10e644be/
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ACTION:display
DESCRIPTION:Talk:Algorithms and Algorithmic Obstacles in High-Dimensional
Regression - David Gamarnik (MIT Sloan School of Management\, USA)
TRIGGER:-PT1H
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