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BEGIN:VEVENT
SUMMARY:Rick Kenyon (Yale)
DTSTART:20200417T170000Z
DTEND:20200417T180000Z
DTSTAMP:20260422T212726Z
UID:PatC/1
DESCRIPTION:Title: Gra
dient models and kappa-harmonic functions\nby Rick Kenyon (Yale) as pa
rt of Probability and the City Seminar\n\n\nAbstract\nThis is joint work w
ith Istvan Prause. \nWe discuss random height models h:R^2 -> R and their
associated limit shapes. A gradient model is one whose surface tension onl
y depends on slope. Examples include the 6- and 8-vertex model and FK-perc
olation models\, among many others. We show that limit shapes for such a m
odel can be explicitly parameterized using kappa-harmonic functions\, that
is\, solutions to the laplacian equation with spatially varying conductan
ce kappa=kappa(x\,y). Here kappa is the square root of the Hessian determi
nant of the surface tension.\n
LOCATION:https://researchseminars.org/talk/PatC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remi Rhodes (Aix-Marseille)
DTSTART:20200424T150000Z
DTEND:20200424T160000Z
DTSTAMP:20260422T212726Z
UID:PatC/2
DESCRIPTION:Title: Con
formal Bootstrap in Liouville theory\nby Remi Rhodes (Aix-Marseille) a
s part of Probability and the City Seminar\n\n\nAbstract\nLiouville confor
mal field theory (denoted LCFT) is a 2-dimensional conformal field theory
depending on a parameter $\\gamma\\in\\R$ and studied since the eighties i
n theoretical physics. In the case of the theory on the Riemann sphere\, p
hysicists proposed closed formulae for the n-point correlation functions u
sing symmetries and representation theory\, called the DOZZ formula (when
n=3) and the conformal bootstrap (for n>3). A probabilistic construction o
f LCFT was recently proposed by David-Kupiainen-Rhodes-Vargas for $\\gamma
\\in (0\,2]$ and the last three authors later proved the DOZZ formula. In
this talk I will present a proof of equivalence between the probabilistic
and the bootstrap construction (proposed in physics) for the n point corr
elation functions with n greater or equal to 4\, valid for $\\gamma\\in (0
\,1)$. Our proof combines the analysis of a natural semi-group\, tools fro
m scattering theory and the use of Virasoro algebra in the context of the
probabilistic approach (the so-called conformal Ward identities).\n\nBased
on joint work with C. Guillarmou\, A. Kupiainen and V. Vargas.\n
LOCATION:https://researchseminars.org/talk/PatC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Alexander (USC)
DTSTART:20200501T160000Z
DTEND:20200501T170000Z
DTSTAMP:20260422T212726Z
UID:PatC/3
DESCRIPTION:Title: Geo
desics\, bigeodesics\, and coalescence in first passage percolation in gen
eral dimension\nby Ken Alexander (USC) as part of Probability and the
City Seminar\n\n\nAbstract\nIn first passage percolation (FPP) on $\\mathb
b{Z}^d$\, i.i.d.~(bond) passage times are attached to the nearest-neighbor
bonds of the lattice\, and the passage time from $x$ to $y$ is the shorte
st sum of bond passage times among all possible paths from $x$ to $y$\; th
e corresponding minimizing path is called a geodesic. One can also conside
r geodesic rays and bigeodesics\, which are one-ended and two-ended infini
te paths for which every finite segment is a geodesic\; a $\\theta$-ray is
a geodesic ray with asymptotic direction $\\theta$. The conjectured pictu
re\, partly verified for $d=2$ under assumptions of various strengths\, is
that for a given $\\theta$\, there is a.s.~a unique $\\theta$--ray from e
ach lattice site\, and any two $\\theta$--rays eventually coalesce\, thoug
h there is a random null set of directions for which this fails\; bigeodes
ics a.s.~do not exist at all. Here we establish portions of this heuristic
picture in higher dimensions (where few results currently exist)\, at lea
st under the assumption that certain very basic but unproven properties of
FPP are valid. We establish a coalescence-like property: taking all the $
\\theta$--rays starting next to a given hyperplane\, and looking at the se
t of points where they cross another hyperplane some distance $r$ ahead of
the starting one\, we show that the geodesics bundle together in the sens
e that the density of the crossing points approaches 0 (at a near-sharp ra
te) as $r\\to\\infty$. This bundling property also holds if we consider to
gether all $\\theta$--rays over a narrow range of directions $\\theta$\, a
nd this fact leads to proof of the absence of bigeodesics. In $d=2$\, bund
ling can be used to bound the probability that two $\\theta$--rays do not
coalesce before traveling a distance $r$.\n
LOCATION:https://researchseminars.org/talk/PatC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Ioffe (Technion)
DTSTART:20200508T140000Z
DTEND:20200508T150000Z
DTSTAMP:20260422T212726Z
UID:PatC/4
DESCRIPTION:Title: Uph
ill diffusions via phase transitions.\nby Dima Ioffe (Technion) as par
t of Probability and the City Seminar\n\n\nAbstract\nUphill diffusions is
an umbrella name for a variety of phenomena when stationary particle curre
nt goes from low density to high density\, in an ostensible violation of F
ick's first law. In this talk I shall present an ongoing joint project wit
h Anna De Masi\, Titti Merola and Errico Presutti\, where uphill diffusion
s are uncovered and described in the context of two dimensional stochastic
phase-field models - a dynamically coupled Ginsburg Landau model and Isin
g model in the phase transition regime.\n
LOCATION:https://researchseminars.org/talk/PatC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Sly (Princeton)
DTSTART:20200515T150000Z
DTEND:20200515T160000Z
DTSTAMP:20260422T212726Z
UID:PatC/5
DESCRIPTION:Title: Cri
tical One-dimensional Multi-particle DLA\nby Allan Sly (Princeton) as
part of Probability and the City Seminar\n\n\nAbstract\nIn multi-particle
Diffusion Limited Aggregation (DLA) a sea of particles perform independent
random walks until they run into the aggregate and are absorbed. In dime
nsion 1\, the rate of growth of the aggregate depends on lambda\, the den
sity of the particles. Kesten and Sidoravicius proved that when $\\lambda
<1$ the aggregate grows like $t^{1/2}$. They furthermore predicted linea
r growth when $\\lambda > 1$ (subsequently confirmed) and $t^{2/3}$ growth
at the critical density $\\lambda =1$. \n\nIn this talk we address the cr
itical case\, confirming the $t^{2/3}$ rate of growth and show that aggreg
ate has a scaling limit whose derivative is a self-similar diffusion proce
ss. Surprisingly this contradicts conjectures on the speed in the mildly
supercritical regime when $\\lambda = 1 + \\epsilon$.\n\nJoint work with D
anny Nam and Dor Elboim\n
LOCATION:https://researchseminars.org/talk/PatC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Sheffield (MIT)
DTSTART:20200529T150000Z
DTEND:20200529T160000Z
DTSTAMP:20260422T212726Z
UID:PatC/6
DESCRIPTION:Title: Pro
bability and pandemics\nby Scott Sheffield (MIT) as part of Probabilit
y and the City Seminar\n\n\nAbstract\nIn one of the simplest epidemic mode
ls\, one lets $p_n$ denote the number of new infections during week $n$ an
d assumes that (during the early stages of the epidemic) $p_{n+1} = R_0 p_
n c_n$ where $c_n$ measures the "fraction of usual contact" that takes pla
ce between people during the nth week. Within this simplistic model\, inte
rmittent strategies (taking $c_n$ small some weeks and large other weeks)
lead to lower infection rates than consistent strategies with the same tot
al amount of contact.\n\nBut what happens if one considers a more realisti
c disease model (such as a SEIR model with multiple compartments\, or a ne
twork-based model\, with empirically based distributions for incubation an
d infection times) and also tries to assign utility to the amount of conta
ct in a more realistic way (accounting for crowding\, social networking an
d other issues)? What factors cause intermittent strategies to outperform
constant strategies? I will discuss a health policy paper I recently co-au
thored with a team of public health researchers that explores this questio
n for a range of simple examples.\n
LOCATION:https://researchseminars.org/talk/PatC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reza Gheissari (U.C. Berkeley)
DTSTART:20200619T170000Z
DTEND:20200619T180000Z
DTSTAMP:20260422T212726Z
UID:PatC/7
DESCRIPTION:Title: Cub
e-root fluctuations and Tracy--Widom tails in critically pre-wetted Ising
interfaces\nby Reza Gheissari (U.C. Berkeley) as part of Probability a
nd the City Seminar\n\n\nAbstract\nConsider the 2D Ising model at low temp
erature on an $N\\times N$ box with minus boundary conditions on the botto
m and plus boundary conditions on the other three sides\, in the presence
of an external field $\\lambda \\ge 0$. Velenik (2004) proved that in the
\\emph{critical pre-wetting} regime of $\\lambda_N \\sim c/N$\, the area c
onfined by the interface is $N^{\\frac{4}{3}+o(1)}$. Since then more refin
ed features of such interfaces---which have been conjectured to converge t
o the Ferrari--Spohn diffusion in critically sized $N^{2/3}\\times N^{1/3}
$ windows--- have only been proven for approximations given by random walk
s under area tilts. \n\nI will discuss recent work with Shirshendu Ganguly
obtaining a more refined understanding of the local and global geometry o
f the Ising interface in the critical pre-wetting regime. As part of this\
, we find that its height fluctuations are truly of order $N^{1/3}$\, and
when they are rescaled by $N^{-1/3}$ they have $\\exp( - \\Theta(x^{3/2}))
$ right tails reminiscent of the Tracy--Widom distribution.\n
LOCATION:https://researchseminars.org/talk/PatC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Toninelli (Vienna)
DTSTART:20200626T140000Z
DTEND:20200626T150000Z
DTSTAMP:20260422T212726Z
UID:PatC/8
DESCRIPTION:Title: The
stationary (2+1)-dimensional AKPZ equation\nby Fabio Toninelli (Vienn
a) as part of Probability and the City Seminar\n\n\nAbstract\nThe AKPZ equ
ation is an anisotropic variant of the celebrated (two-dimensional) KPZ st
ochastic PDE\, which is expected to describe the large-scale behavior of (
2+1)-dimensional growth models whose average speed of growth is a non-conv
ex function of the average slope (AKPZ universality class). Several intera
cting particle systems belonging to the AKPZ class are known\, notably a c
lass of two-dimensional interlaced particle systems introduced by A. Borod
in and P. Ferrari.\n\nIn the physics literature\, the AKPZ equation was co
njectured to have the same large-scale behavior as the stochastic heat equ
ation with additive noise (2d-SHE). In this talk\, I will show that this i
s not really true: in fact\, the stationary equation is not invariant unde
r diffusive rescaling (as the 2d-SHE is)\, not even asymptotically on larg
e scales\, and logarithmic corrections in the scaling are needed instead.
[Based on joint work with G. Cannizzaro and D. Erhard]\n
LOCATION:https://researchseminars.org/talk/PatC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Penington (Bath)
DTSTART:20201016T163000Z
DTEND:20201016T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/10
DESCRIPTION:Title: Br
ownian bees in the infinite swarm limit\nby Sarah Penington (Bath) as
part of Probability and the City Seminar\n\n\nAbstract\nConsider a system
of $N$ particles moving according to Brownian motions and branching at rat
e one. Each time a particle branches\, the particle in the system furthest
from the origin is killed. The large $N$ and large time behaviour of the
system is related to solutions of a novel non-linear free boundary partial
differential equation. Based on joint work with Julien Berestycki\, Éric
Brunet and Jim Nolen.\n
LOCATION:https://researchseminars.org/talk/PatC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (Toronto)
DTSTART:20201023T163000Z
DTEND:20201023T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/11
DESCRIPTION:Title: Co
nvergence of finite range exclusions and KPZ equation to the KPZ fixed poi
nt\nby Jeremy Quastel (Toronto) as part of Probability and the City Se
minar\n\n\nAbstract\nWe will describe a method of comparison with TASEP wh
ich proves that both the KPZ equation and finite range exclusion models co
nverge to the KPZ fixed point. For the KPZ equation and the nearest neigh
bour exclusion\, the initial data is allowed to be a continuous function p
lus a finite number of narrow wedges\, but for non-nearest neighbour exclu
sions\, one needs at the present time some randomization of the initial da
ta. We will give a little background\, but the talk will mostly be about
the proof. Joint work with Sourav Sarkar.\n
LOCATION:https://researchseminars.org/talk/PatC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (Freie Universität Berlin)
DTSTART:20201030T163000Z
DTEND:20201030T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/12
DESCRIPTION:Title: Ma
ss asymptotics for the 2d parabolic Anderson model with space white noise
potential\nby Nicolas Perkowski (Freie Universität Berlin) as part of
Probability and the City Seminar\n\n\nAbstract\nWe study the long time be
havior of the total mass of the 2d parabolic Anderson model (PAM) with whi
te noise potential\, which is the universal scaling limit of 2d branching
random walks in small random environments. There are several known results
on the long time behavior of the PAM for more regular potentials\, but th
e 2d white noise is very singular and it requires renormalization techniqu
es. In particular\, the Feynman-Kac representation\, usually the main tool
for deriving asymptotics\, breaks down. To overcome this problem we use a
measure transform and we introduce a new "partial Feynman-Kac representat
ion“. The new representation is based on a diffusion with distributional
drift\, and we derive Gaussian heat kernel bounds for such diffusions. Ba
sed on joint works with Wolfgang König and Willem van Zuijlen.\n
LOCATION:https://researchseminars.org/talk/PatC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (NYU Courant)
DTSTART:20201204T173000Z
DTEND:20201204T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/13
DESCRIPTION:Title: Mi
croscopic description of Coulomb gases\nby Sylvia Serfaty (NYU Courant
) as part of Probability and the City Seminar\n\n\nAbstract\nWe are intere
sted in the statistical mechanics of systems of N points with Coulomb inte
ractions in general dimension for a broad temperature range.\nWe discuss l
ocal laws characterizing the rigidity of the system at the microscopic lev
el\, as well as free energy expansion and Central Limit Theorems for fluct
uations.\n
LOCATION:https://researchseminars.org/talk/PatC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Damron (Georgia Tech)
DTSTART:20201211T173000Z
DTEND:20201211T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/14
DESCRIPTION:Title: Cr
itical first-passage percolation in two dimensions\nby Michael Damron
(Georgia Tech) as part of Probability and the City Seminar\n\n\nAbstract\n
In 2d first-passage percolation (FPP)\, we place nonnegative i.i.d. weight
s (t_e) on the edges of Z^2 and study the induced weighted graph pseudomet
ric T = T(x\,y) If we denote by p = P(t_e = 0)\, then there is a transitio
n in the large-scale behavior of the model as p varies from 0 to 1. When p
< 1/2\, T(0\,x) grows linearly in x\, and when p > 1/2\, it is stochastic
ally bounded. The critical case\, where p = 1/2\, is more subtle\, and the
sublinear growth of T(0\,x) depends on the behavior of the distribution f
unction of t_e near zero. I will discuss my work over the past few years t
hat (a) determines the exact rate of growth of T(0\,x)\, (b) determines th
e "time constant" for the site-FPP model on the triangular lattice and\, m
ore recently (c) studies the growth of T(0\,x) in a dynamical version of t
he model\, where weights are resampled according to independent exponentia
l clocks. These are joint works with J. Hanson\, D. Harper\, W.-K. Lam\, P
. Tang\, and X. Wang.\n
LOCATION:https://researchseminars.org/talk/PatC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-François Le Gall (Paris-Saclay)
DTSTART:20201106T173000Z
DTEND:20201106T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/20
DESCRIPTION:Title: Co
mpact and non-compact models of random geometry\nby Jean-François Le
Gall (Paris-Saclay) as part of Probability and the City Seminar\n\n\nAbstr
act\nWe discuss various models of random geometry that arise as scaling
limits of large planar graphs embedded in the 2-sphere (also called pla
nar maps). The most popular compact models are the Brownian sphere or
Brownian map\, and the Brownian disk\, which is the scaling limit o
f planar maps with a boundary. We explain how Brownian disks can be
viewed as connected components of the complement of balls in the Brown
ian sphere\, and we discuss a remarkable growth-fragmentation process t
hat describes the evolution of the boundary sizes of these component
s when the radius of the ball increases. We also introduce the non-comp
act models called the Brownian plane\, the infinite Brownian disk an
d the Brownian half-plane\, and we present a unified construction of
these three models based on a spine decomposition. Most of the tal
k is based on joint work with Armand Riera.\n
LOCATION:https://researchseminars.org/talk/PatC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhan Aru (EPFL Lausanne)
DTSTART:20201113T173000Z
DTEND:20201113T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/21
DESCRIPTION:Title: Im
aginary multiplicative chaos: different questions from different contexts\
, and a few answers too\nby Juhan Aru (EPFL Lausanne) as part of Proba
bility and the City Seminar\n\n\nAbstract\nImaginary multiplicative chaos
is formally given by exp(iG)\, where G is a log-correlated Gaussian field
in d dimensions.\nIt comes up in several different contexts. For example\n
- as a analytic continuation of the real multiplicative chaos\, that is ce
ntral in the probabilistic study of Liouville quantum gravity and Liouvill
e CFT\;\n- when taking the continuum limit of the spin field for the XOR-I
sing model\;\n- in relation to the Kosterlitz-Thouless-type of phase trans
itions.\nIn this talk I will try to explain how imaginary chaos comes up i
n these contexts\, which questions it brings along\, and how to answer som
e of these questions. \nThis is a joint work with J. Junnila\, and also pa
rtly with A. Jego.\n
LOCATION:https://researchseminars.org/talk/PatC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Ahn (MIT)
DTSTART:20201002T163000Z
DTEND:20201002T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/22
DESCRIPTION:by Andrew Ahn (MIT) as part of Probability and the City Semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PatC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Kosygina (Baruch College and the CUNY Graduate Center)
DTSTART:20210402T163000Z
DTEND:20210402T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/23
DESCRIPTION:Title: Fr
om generalized Ray-Knight theorems to functional CLTs for some models of s
elf-interacting random walks on Z\nby Elena Kosygina (Baruch College a
nd the CUNY Graduate Center) as part of Probability and the City Seminar\n
\n\nAbstract\nIn several models of self-interacting random walks (SIRWs) o
n Z generalized Ray-Knight theorems for local times proved to be a very us
eful tool for studying the limiting behavior of these walks. Examples incl
ude some reinforced random walks\, asymptotically free and polynomially se
lf-repelling random walks\, excited random walks\, rotor walks with defect
s. I shall give an overview of some of these models and then concentrate o
n the joint work with Thomas Mountford (EPFL) and Jon Peterson (Purdue Uni
versity) on the functional limit theorem for recurrent excited random walk
s with Markovian cookie stacks.\n
LOCATION:https://researchseminars.org/talk/PatC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Cook (Duke)
DTSTART:20210122T173000Z
DTEND:20210122T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/24
DESCRIPTION:Title: Un
iversality for the minimum modulus of random trigonometric polynomials
\nby Nick Cook (Duke) as part of Probability and the City Seminar\n\n\nAbs
tract\nWe consider the restriction to the unit circle of random degree-n p
olynomials with iid normalized coefficients (Kac polynomials). Recent work
of Yakir and Zeitouni shows that for Gaussian coefficients\, the minimum
modulus (suitably rescaled) follows a limiting exponential distribution. W
e show this is a universal phenomenon\, extending their result to arbitrar
y sub-Gaussian coefficients\, such as Rademacher signs. For discrete distr
ibutions we must now deal with possible arithmetic structure in the polyno
mial evaluated at different points of the circle. On "minor arcs" we obtai
n strong comparisons with the Gaussian model by translating to a random wa
lk in a high dimensional phase space\, and obtaining strong decay estimate
s on characteristic functions\, while major arcs can be handled with crude
r arguments. Based on joint work with Hoi Nguyen.\n
LOCATION:https://researchseminars.org/talk/PatC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Pain (NYU Courant)
DTSTART:20210129T173000Z
DTEND:20210129T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/25
DESCRIPTION:Title: Op
timal local law and central limit theorem for beta-ensembles\nby Miche
l Pain (NYU Courant) as part of Probability and the City Seminar\n\n\nAbst
ract\nIn this talk\, I will present a joint work with Paul Bourgade and Kr
ishnan Mody. We consider beta-ensembles with general potentials (or equiva
lently a log-gas in dimension 1)\, which are a generalization of Gaussian
beta-ensembles and of classical invariant ensembles of random matrices. We
prove a multivariate central limit theorem for the logarithm of the chara
cteristic polynomial\, showing that it behaves as a log-correlated field.
A key ingredient is an optimally sharp local law for the the Stieljes tran
sform of the empirical measure which can be of independent interest. Both
the proofs of the CLT and the local law are based essentially on loop equa
tions techniques.\n
LOCATION:https://researchseminars.org/talk/PatC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Garban (Lyon)
DTSTART:20210205T173000Z
DTEND:20210205T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/26
DESCRIPTION:Title: Vo
rtex fluctuations in continuous spin systems and lattice gauge theory\
nby Christophe Garban (Lyon) as part of Probability and the City Seminar\n
\n\nAbstract\nTopological phase transitions were discovered by Berezinskii
-Kosterlitz-Thouless (BKT) in the 70's. They describe intriguing phase tra
nsitions for classical statistical physics models such as\n\n - the 2d XY
model (spins on Z^2 with values in the unit circle)\n\n - the 2d Coulomb g
as\n\n - the integer-valued Gaussian Free Field (or Z-ferromagnet)\n\n - A
belian lattice gauge theory on Z^4\n\nIn this talk\, I will explain a new
technique to obtain quantitative lower bounds on the fluctuations induced
by the topological defects (vortices) on such systems at low temperature.
We will see in particular that the fluctuations generated by the vortices
are at least of the same order of magnitude as the ones produced by the so
-called "spin-wave". Our approach is non-perturbative but it gives matchin
g lower bounds with the fluctuations predicted from RG analysis. I will st
art the talk by giving an overview of the above models. The talk is based
on joint works with Avelio Sepúlveda.\n
LOCATION:https://researchseminars.org/talk/PatC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Shen (Wisconsin)
DTSTART:20210212T173000Z
DTEND:20210212T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/27
DESCRIPTION:Title: St
ochastic quantization\, large N\, and mean field limit\nby Hao Shen (W
isconsin) as part of Probability and the City Seminar\n\n\nAbstract\nWe st
udy "large N problems” in quantum field theory using SPDE methods via st
ochastic quantization. In the SPDE setting this is formulated as mean fiel
d problems. We will consider the vector Phi^4 model (i.e. linear sigma mod
el)\, whose stochastic quantization is a system of N coupled dynamical Phi
^4 SPDEs. We discuss a series of results. First\, in 2D\, we prove mean fi
eld limit for these dynamics as N goes to infinity. We also show that the
quantum field theory converges to massive Gaussian free field in this limi
t\, in both 2D and 3D. Moreover we prove exact formulae for some correlati
ons of O(N)-invariant observables in the large N limit\; such formulae wer
e predicted using “bubble diagrams” in physics.\n
LOCATION:https://researchseminars.org/talk/PatC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Hammond (UC Berkeley)
DTSTART:20210312T173000Z
DTEND:20210312T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/29
DESCRIPTION:Title: St
ability and chaos in dynamical last passage percolation\nby Alan Hammo
nd (UC Berkeley) as part of Probability and the City Seminar\n\n\nAbstract
\nMany complex statistical mechanical models have intricate energy landsca
pes. The ground state\, or lowest energy state\, lies at the base of the d
eepest valley. In examples such as spin glasses and Gaussian polymers\, th
ere are many valleys\; the abundance of near-ground states (at the base of
valleys) indicates the phenomenon of chaos\, under which the ground state
alters profoundly when the model's disorder is slightly perturbed. Indeed
\, a monograph of Sourav Chatterjee from 2014 establishes that\, for a cla
ss of models of Gaussian disorder\, this abundance of competing minimizers
is accompanied both by a rapid outset of chaos under perturbation of the
system by noise\, and by the effect of super-concentration\, in which mod
el statistics have lower variance than in classical scenarios\, for which
a central limit theorem may apply.\n\nIn this talk\, a recent investigatio
n\, jointly undertaken with Shirshendu Ganguly\, of a natural dynamics for
a model of planar last passage percolation will be discussed. Robust prob
abilistic and geometric technique permits a very quantified analysis of th
e presence of close rivals in energy to the ground state for the static ve
rsion of the model\; consequently\, the order of the scale that heralds th
e transition from stability to chaos for the dynamical model is identified
. The tools that drive the investigation include harmonic analytic techniq
ue present in Chatterjee's work\, and the use of Brownian Gibbs resampling
analysis for random ensembles of curves naturally associated to last pass
age percolation via the Robinson-Schensted-Knuth correspondence.\n
LOCATION:https://researchseminars.org/talk/PatC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Maas (IST Austria)
DTSTART:20210319T163000Z
DTEND:20210319T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/30
DESCRIPTION:Title: Ho
mogenisation of discrete dynamical optimal transport\nby Jan Maas (IST
Austria) as part of Probability and the City Seminar\n\n\nAbstract\nMany
stochastic systems can be viewed as gradient flow ('steepest descent') in
the space of probability measures\, where the driving functional is a rela
tive entropy and the relevant geometry is described by a dynamical optimal
transport problem. In this talk we focus on these optimal transport probl
ems and describe recent work on the limit passage from discrete to continu
ous.\n\nSurprisingly\, it turns out that discrete transport metrics may fa
il to converge to the expected limit\, even when the associated gradient f
lows converge. We will illustrate this phenomenon in examples and present
a recent homogenisation result.\n\nThis talk is based on joint work with P
eter Gladbach\, Eva Kopfer\, and Lorenzo Portinale.\n
LOCATION:https://researchseminars.org/talk/PatC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bufetov (Bonn)
DTSTART:20210219T173000Z
DTEND:20210219T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/31
DESCRIPTION:Title: Cu
toff profile of ASEP on a segment\nby Alexey Bufetov (Bonn) as part of
Probability and the City Seminar\n\n\nAbstract\nThe mixing behavior of th
e Asymmetric Simple Exclusion Process (=ASEP) on a segment will be discuss
ed. We will show that its cutoff profile is given by the Tracy-Widom distr
ibution function\, which extends earlier results of Labbe-Lacoin and Benja
mini-Berger-Hoffman-Mossel. We will also discuss a multi-species version o
f this model (also known as a biased card shuffling or an oriented swap pr
ocess). The talk is based on joint works with P. Nejjar and with V. Gorin\
, D. Romik.\n
LOCATION:https://researchseminars.org/talk/PatC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveliina Peltola (Bonn)
DTSTART:20210305T173000Z
DTEND:20210305T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/32
DESCRIPTION:Title: On
large deviations of SLEs\, real rational functions\, and zeta-regularized
determinants of Laplacians\nby Eveliina Peltola (Bonn) as part of Pro
bability and the City Seminar\n\n\nAbstract\nThe talk concerns a large dev
iation principle (LDP) for (multiple) Schramm-Loewner evolution (SLE) curv
es for the Hausdorff metric.\nWhen studying the LDP\, we introduced a ''Lo
ewner potential'' that describes the rate function.\nThis object turned ou
t to have several intrinsic\, and perhaps surprising\, connections to vari
ous fields.\nFor instance\, it has a simple expression in terms of zeta-re
gularized determinants of Laplace-Beltrami operators.\nOn the other hand\,
minima of the Loewner potential solve a nonlinear first order PDE that ar
ises\nin a semiclassical limit of certain correlation functions in conform
al field theory (arguably also related to isomonodromic systems).\nFinally
\, the Loewner potential minimizers classify rational functions with real
critical points\, thereby providing a novel proof for\na version of the no
w well-known Shapiro-Shapiro conjecture in real enumerative geometry. This
talk is based on joint work with Yilin Wang (MIT).\n
LOCATION:https://researchseminars.org/talk/PatC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Bodineau (École Polytechnique)
DTSTART:20210409T163000Z
DTEND:20210409T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/33
DESCRIPTION:Title: Fl
uctuating Boltzmann equation and large deviations for a hard sphere gas\nby Thierry Bodineau (École Polytechnique) as part of Probability and t
he City Seminar\n\n\nAbstract\nA gas dynamics can be modelled by a billiar
d made of hard spheres\, moving according to the laws of classical mechani
cs. Initially the spheres are randomly distributed according to a probabil
ity measure which is then transported by the flow of the deterministic dyn
amics. Since the seminal work of Lanford\, it is known in the kinetic limi
t that the gas density converges towards the Boltzmann equation (at least
for a short time). \n\nIn this talk\, we are going to discuss the fluctuat
ions of the microscopic dynamics around the Boltzmann equation and the con
vergence of the fluctuation field to the fluctuating Boltzmann equation. W
e will also show that the occurence of atypical evolutions can be quantifi
ed by a large deviation principle. This analysis relies on the study of th
e correlations created by the Hamiltonian dynamics. We will see that the e
mergence of irreversibility in the kinetic limit can be related to the sin
gularity of these correlations.\n\nZoom meeting ID: 991 4448 8133\, passwo
rd: 800920\n
LOCATION:https://researchseminars.org/talk/PatC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Angel (UBC)
DTSTART:20210326T163000Z
DTEND:20210326T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/34
DESCRIPTION:Title: A
tale of two balloons\nby Omer Angel (UBC) as part of Probability and t
he City Seminar\n\n\nAbstract\nWe study the following process\, motivated
by coalescing random\nwalks: From each point of a Poisson point process st
art growing a\nballoon at rate 1. When two balloons touch\, they pop and d
isappear. We\nstudy this on various spaces and various starting states. En
route we\nfind a new(ish) 0-1 law\, and generalize bounds on independent
sets that\nare factors of IID. Joint work with Gourab Ray and Yinon Spinka
.\n
LOCATION:https://researchseminars.org/talk/PatC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Dauvergne (Princeton)
DTSTART:20210226T173000Z
DTEND:20210226T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/35
DESCRIPTION:Title: Le
arning from the directed landscape\nby Duncan Dauvergne (Princeton) as
part of Probability and the City Seminar\n\n\nAbstract\nThe directed land
scape is a random `directed metric' on the \nspacetime plane that arises a
s the scaling limit of integrable models \nof last passage percolation. It
is expected to be the universal \nscaling limit for all models in the KPZ
universality class for random \ngrowth. In this talk\, I will describe it
s construction in terms of the \nAiry line ensemble\, give an extension of
this construction for optimal \nlength disjoint paths in the directed lan
dscape\, and show how these \nconstructions reveal surprising Brownian str
uctures in the directed \nlandscape. Based on joint work with J. Ortmann\,
B. Virag\, and L. Zhang.\n
LOCATION:https://researchseminars.org/talk/PatC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Wu (NYU Shanghai)
DTSTART:20210416T140000Z
DTEND:20210416T150000Z
DTSTAMP:20260422T212726Z
UID:PatC/36
DESCRIPTION:Title: Ma
ssless phases for the Villain model in d>=3\nby Wei Wu (NYU Shanghai)
as part of Probability and the City Seminar\n\n\nAbstract\nThe XY and the
Villain models are mathematical idealization of real world models of liqui
d crystal\, liquid helium\, and superconductors. Their phase transition ha
s important applications in condensed matter physics and led to the Nobel
Prize in Physics in 2016. However we are still far from a complete mathem
atical understanding of the transition. The spin wave conjecture\, origina
lly proposed by Dyson and by Mermin and Wagner\, predicts that at low temp
erature\, large scale behaviors of these models are closely related to Gau
ssian free fields. I will review the historical background and discuss so
me recent progress on this conjecture in d>=3. Based on the joint work wit
h Paul Dario (Tel Aviv).\n
LOCATION:https://researchseminars.org/talk/PatC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeni Dimitrov (Columbia)
DTSTART:20210423T163000Z
DTEND:20210423T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/37
DESCRIPTION:Title: To
wards universality for Gibbsian line ensembles\nby Evgeni Dimitrov (Co
lumbia) as part of Probability and the City Seminar\n\n\nAbstract\nGibbsia
n line ensembles are natural objects that arise in statistical mechanics m
odels of random tilings\, directed polymers\, random plane partitions and
avoiding random walks. In this talk I will discuss a general framework for
establishing universal KPZ scaling limits for sequences of Gibbsian line
ensembles. This framework is still being developed and I will explain some
of the recent progress that has been made towards carrying it our for two
integrable models of random Hall-Littlewood plane partitions and log-gamm
a polymers.\n
LOCATION:https://researchseminars.org/talk/PatC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Matetski (Columbia)
DTSTART:20210514T163000Z
DTEND:20210514T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/38
DESCRIPTION:Title: Di
rected mean curvature flow in noisy environment\nby Konstantin Matetsk
i (Columbia) as part of Probability and the City Seminar\n\n\nAbstract\nWe
consider the directed mean curvature flow evolving on the plane in a weak
disordered Gaussian environment. A simpler version of the model is the qu
enched KPZ equation with a weak noise. We prove that\, when started from a
sufficiently regular initial state\, a rescaled and renormalized curve co
nverges to the Cole–Hopf solution of the KPZ equation. This is a joint w
ork with A.Gerasimovičs and M. Hairer.\n
LOCATION:https://researchseminars.org/talk/PatC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cannizzaro (Warwick)
DTSTART:20210521T163000Z
DTEND:20210521T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/39
DESCRIPTION:Title: Ed
wards-Wilkinson fluctuations for the Anisotropic KPZ in the weak coupling
regime\nby Giuseppe Cannizzaro (Warwick) as part of Probability and th
e City Seminar\n\n\nAbstract\nIn this talk\, we present recent results on
an anisotropic variant of the Kardar-Parisi-Zhang equation\, the Anisotrop
ic KPZ equation (AKPZ)\, in the critical spatial dimension d=2. This is a
singular SPDE which is conjectured to capture the behaviour of the fluctua
tions of a large family of random surface growth phenomena but whose analy
sis falls outside of the scope not only of classical stochastic calculus b
ut also of the theory of Regularity Structures and paracontrolled calculus
. We first prove the conjecture made in [Cannizzaro\, Erhard\, Toninelli\,
"The AKPZ equation at stationarity: logarithmic superdiffusivity"]\, i.e.
we show that the nonlinearity causes a logarithmically superdiffusive beh
aviour at large scales and more precisely that correlation length of the s
olution grows like t1/2 (log t)1/4 up to lower order correction. Motivated
by the previous\, we consider the AKPZ equation in the so-called weak cou
pling regime\, i.e. the equation regularised at scale N and the coefficien
t of the nonlinearity tuned down by a factor (log N)-1/2\, and prove that\
, for N going to infinity\, its solution converges to a linear stochastic
heat equation with renormalised coefficients.\nThe talk is based on (ongoi
ng) joint work with D. Erhard and F. Toninelli.\n
LOCATION:https://researchseminars.org/talk/PatC/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Gu (Carnegie Mellon University)
DTSTART:20210430T163000Z
DTEND:20210430T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/40
DESCRIPTION:Title: A
CLT for KPZ on torus\nby Yu Gu (Carnegie Mellon University) as part of
Probability and the City Seminar\n\n\nAbstract\nI will present a joint wo
rk with Tomasz Komorowski on proving Gaussian fluctuations for the KPZ equ
ation on the torus.\n
LOCATION:https://researchseminars.org/talk/PatC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramon van Handel (Princeton)
DTSTART:20210917T163000Z
DTEND:20210917T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/41
DESCRIPTION:Title: Sh
arp matrix concentration inequalities\nby Ramon van Handel (Princeton)
as part of Probability and the City Seminar\n\n\nAbstract\nWhat does the
spectrum of a random matrix look like when we make no\nassumption whatsoev
er about the covariance pattern of its entries? It may\nappear hopeless t
hat anything useful can be said at this level of\ngenerality. Nonetheless\
, a set of tools known as "matrix concentration\ninequalities" makes it po
ssible to estimate at least the spectral norm of\nvery general random matr
ices up to logarithmic factors in the dimension.\nOn the other hand\, it i
s well known that these inequalities fail to yield\nsharp results for even
the simplest random matrix models.\n\nIn this talk I will describe a powe
rful new class of matrix concentration\ninequalities that achieve optimal
results in many situations that are\noutside the reach of classical method
s. Our results are easily applicable\nin concrete examples\, and yield det
ailed nonasymptotic information on the\nfull spectrum of essentially arbit
rarily structured random matrices. These\nnew inequalities arise from an u
nexpected phenomenon: the spectrum of\nrandom matrices is accurately captu
red by certain predictions of free\nprobability theory under surprisingly
minimal assumptions. Our proofs\nquantify the notion that it costs little
to be free.\n\nThe talk is based on joint works with Afonso Bandeira and M
arch\nBoedihardjo\, and with Tatiana Brailovskaya. No prior background wil
l be\nassumed.\n
LOCATION:https://researchseminars.org/talk/PatC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Chatterjee (Stanford)
DTSTART:20211001T163000Z
DTEND:20211001T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/42
DESCRIPTION:Title: Lo
cal KPZ behavior under arbitrary scaling limits\nby Sourav Chatterjee
(Stanford) as part of Probability and the City Seminar\n\n\nAbstract\nOne
of the main difficulties in proving convergence of discrete models of surf
ace growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher
than one is that the correct way to take a scaling limit\, so that the lim
it is nontrivial\, is not known in a rigorous sense. The same problem has
so far prevented the construction of nontrivial solutions of the KPZ equat
ion in dimensions higher than one. To understand KPZ growth without being
hindered by this issue\, I will introduce a new concept in this talk\, cal
led "local KPZ behavior"\, which roughly means that the instantaneous grow
th of the surface at a point decomposes into the sum of a Laplacian term\,
a gradient squared term\, a noise term\, and a remainder term that is neg
ligible compared to the other three terms and their sum. The main result i
s that for a general class of surfaces\, which contains the model of direc
ted polymers in a random environment as a special case\, local KPZ behavio
r occurs under arbitrary scaling limits\, in any dimension.\n
LOCATION:https://researchseminars.org/talk/PatC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Titus Lupu (CNRS and Sorbonne Université)
DTSTART:20210924T163000Z
DTEND:20210924T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/43
DESCRIPTION:Title: Mu
ltiplicative chaos of the 2D Brownian loop soup\nby Titus Lupu (CNRS a
nd Sorbonne Université) as part of Probability and the City Seminar\n\n\n
Abstract\nIt is known from the works in Mathematical Physics that the cont
inuum Gaussian free field (GFF) admits representations in terms of occupat
ion measures of Brownian trajectories. In particular\, the square of the G
FF (suitably renormalized) has the same distribution as the occupation mea
sure of a Poisson point process of Brownian loops\, known as the Brownian
loop soup. This is the Le Jan's isomorphism theorem. The Brownian loop sou
ps come with an intensity parameter $\\theta >0$\, and the connection to t
he GFF is for the particular parameter $\\theta=1/2$. In our work we relat
ed the theory of the Gaussian Multiplicative Chaos (GMC) in 2D (renormaliz
ed exponential of the 2D continuum GFF\, also appearing in Liouville field
theory) to the 2D Brownian loop soup. Actually we constructed a so called
multiplicative chaos of the Brownian loop soup for every intensity parame
ter $\\theta$. Compared to the multiplicative chaos of a single 2D Brownia
n trajectory\, which has been first constructed by Bass\, Burdzy and Khosh
nevisan in the 90s\, in our work we require an additional layer of renorma
lization due to ultraviolet divergence in the Brownian loop soup. For the
particular parameter $\\theta=1/2$\, our multiplicative chaos of the Brown
ian loop soup has the same distribution as the renormalized hyperbolic cos
ine of the GFF\, i.e. is a sum of two GMCs. For other intensity parameters
$\\theta$ we obtain new non-Gaussian multiplicative chaoses\, which satis
fy moreover a covariance property under conformal transformations of the d
omain. This is joint work with Elie Aïdekon (Sorbonne Université/Fudan U
niversity)\, Nathanael Berestycki (University of Vienna) and Antoine Jégo
(University of Vienna).\n
LOCATION:https://researchseminars.org/talk/PatC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arjun Krishnan (Rochester)
DTSTART:20211015T163000Z
DTEND:20211015T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/44
DESCRIPTION:Title: Co
rrelations of Busemann functions and the 2nd KPZ relationship\nby Arju
n Krishnan (Rochester) as part of Probability and the City Seminar\n\n\nAb
stract\nBusemann functions (correctors in homogenization theory) are objec
ts of interest in first- and last-passage percolation. Determining the cor
relations of Busemann function increments is important because of its rela
tionship to the second KPZ relationship that relates the two fluctuation e
xponents in the models. We show that the correlations of adjacent Busemann
increments in last-passage percolation with general weights are directly
related to the time-constant of last-passage percolation with exponential
weights (an integrable model). Using this relationship\, we give an easily
checkable condition that determines when adjacent Busemann increments are
negatively correlated\, and prove that\, for example\, last-passage perco
lation with iid Bernoulli weights has negatively correlated adjacent Busem
ann increments.\n\nJoint work with I. Alevy\n
LOCATION:https://researchseminars.org/talk/PatC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morris Ang (MIT)
DTSTART:20211105T163000Z
DTEND:20211105T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/45
DESCRIPTION:Title: In
tegrability of the conformal loop ensemble\nby Morris Ang (MIT) as par
t of Probability and the City Seminar\n\n\nAbstract\nFor 8/3 < κ < 8\, th
e conformal loop ensemble CLEκ is a canonical random ensemble of loops wh
ich is conformally invariant in law\, and whose loops locally look like Sc
hramm-Loewner evolution with parameter κ. It describes the scaling limits
of the Ising model\, percolation\, and other models. When κ ≤ 4 the lo
ops are simple curves. In this regime we compute the three-point nesting s
tatistic of CLEκ on the sphere\, and show it agrees with the imaginary DO
ZZ formula of Zamolodchikov (2005). We also obtain the expression of the
(properly normalized) probability that three points are on the same CLE lo
op in terms of the DOZZ formula. The analogous quantity for three points o
n the same cluster was previously conjectured by Delfino and Viti. To our
best knowledge our formula has not been predicted in the physics literatur
e. Our arguments depend on couplings of CLE with Liouville quantum gravit
y and the integrability of Liouville conformal field theory. Based on join
t work with Xin Sun.\n
LOCATION:https://researchseminars.org/talk/PatC/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Chiarini (Eindhoven University of Technology)
DTSTART:20211112T173000Z
DTEND:20211112T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/46
DESCRIPTION:Title: Di
sconnection and entropic repulsion for the harmonic crystal with random co
nductances\nby Alberto Chiarini (Eindhoven University of Technology) a
s part of Probability and the City Seminar\n\n\nAbstract\nWe study level-s
et percolation of the discrete Gaussian free field on the Euclidean lattic
e in three and more dimensions\, equipped with uniformly elliptic random c
onductances. We prove that this percolation model undergoes a non-trivial
phase transition at a deterministic level. For a compact set A in \\mathbb
{R}^d\, we study the disconnection event that the level-set of the field b
elow a given level disconnects the discrete blow-up of A from the boundary
of an enclosing box\, in a strongly percolative regime. We present quench
ed asymptotic upper and lower bounds on this probability in terms of the h
omogenized capacity of A. The upper and lower bounds concerning disconnect
ion that we derive are plausibly matching at leading order. In this case\,
this work shows that conditioning on disconnection leads to an entropic p
ush-down of the field. (Based on a joint work with M. Nitzschner NYU Coura
nt)\n
LOCATION:https://researchseminars.org/talk/PatC/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingfu Zhang (Princeton)
DTSTART:20211029T163000Z
DTEND:20211029T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/47
DESCRIPTION:Title: Th
e environment seen from a geodesic in last-passage percolation\nby Lin
gfu Zhang (Princeton) as part of Probability and the City Seminar\n\n\nAbs
tract\nIn exponential directed last-passage percolation\, each vertex in Z
^2 is assigned an i.i.d. exponential weight\, and the geodesic between a p
air of vertices refers to the up-right path connecting them\, with the max
imum total weight along the path. It is a natural question to ask what a g
eodesic looks like locally\, and how weights on and nearby the geodesic be
have. In this talk\, I will present some new results on this. We show conv
ergence of the distribution of the ‘environment’ as seen from a typica
l point along the geodesic\, and convergence of the corresponding empirica
l measure\, as the geodesic length goes to infinity. In addition\, we obta
in an explicit description of the limiting environment\, which depends on
the direction of the geodesic. This in principle enables one to compute al
l the local statistics of the geodesic\, and I will talk about some surpri
sing and interesting examples. This is based on joint work with James Mart
in and Allan Sly.\n
LOCATION:https://researchseminars.org/talk/PatC/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firas Rassoul-Agha (Utah)
DTSTART:20211210T173000Z
DTEND:20211210T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/48
DESCRIPTION:Title: Ge
odesic Length in First-Passage Percolation\nby Firas Rassoul-Agha (Uta
h) as part of Probability and the City Seminar\n\n\nAbstract\nWe study fir
st-passage percolation through related optimization problems over paths of
restricted length. The path length variable is in duality with a shift of
the weights. This puts into a convex duality framework old observations a
bout the convergence of the normalized Euclidean length of geodesics due t
o Hammersley and Welsh\, Smythe and Wierman\, and Kesten\, and leads to ne
w results about geodesic length and the regularity of the shape function a
s a function of the weight shift. For points far enough away from the orig
in\, the ratio of the geodesic length and the $\\ell^1$ distance to the en
dpoint is uniformly bounded away from one. The shape function is a strictl
y concave function of the weight shift. Atoms of the weight distribution g
enerate singularities\, that is\, points of nondifferentiability\, in this
function. We generalize to all distributions\, directions and dimensions
an old singularity result of Steele and Zhang for the planar Bernoulli cas
e. When the weight distribution has two or more atoms\, a dense set of shi
fts produce singularities. The results come from a combination of the conv
ex duality\, the shape theorems of the different first-passage optimizatio
n problems\, and modification arguments. This is joint work with Arjun Kri
shnan and Timo Seppalainen.\n
LOCATION:https://researchseminars.org/talk/PatC/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milind Hegde (UC Berkeley)
DTSTART:20211008T163000Z
DTEND:20211008T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/49
DESCRIPTION:Title: Br
ownianity in KPZ\nby Milind Hegde (UC Berkeley) as part of Probability
and the City Seminar\n\n\nAbstract\nThe KPZ universality class is believe
d to contain a very broad collection of models of stochastic growth. A the
me in KPZ that has developed a great deal over the last 15 years\, and par
ticularly in recent years\, is the presence of Brownian behaviour---the cl
assical kind of universality---in many natural objects. In this talk I wil
l survey some of the results in the zero-temperature setting---concerning
objects such as last passage percolation\, the Airy_2 process\, and the KP
Z fixed point---focusing on recent advances in obtaining and applying quan
titative process-level Brownian comparisons of the Airy_2 process\, as wel
l as connections to the behaviour of geodesics in last passage percolation
. Based on joint work with Jacob Calvert\, Ivan Corwin\, Alan Hammond\, an
d Konstantin Matetski.\n
LOCATION:https://researchseminars.org/talk/PatC/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Yang (Stanford)
DTSTART:20211203T173000Z
DTEND:20211203T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/50
DESCRIPTION:Title: KP
Z and Boltzmann-Gibbs\nby Kevin Yang (Stanford) as part of Probability
and the City Seminar\n\n\nAbstract\nThe KPZ equation is a stochastic PDE
whose derivative conjecturally provides a universal model for "hydrodynami
c fluctuations". This is one version of the weak KPZ universality conjectu
re\, which has drawn significant attention in the past few decades. We wil
l discuss recent work on this conjecture for hydrodynamic limit fluctuatio
ns of general interacting particle systems. The key ingredient is a Boltzm
ann-Gibbs principle for general systems\, whose applications beyond KPZ an
d whose potential refinements will both be discussed as well.\n
LOCATION:https://researchseminars.org/talk/PatC/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin McSwiggen (NYU)
DTSTART:20211022T163000Z
DTEND:20211022T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/51
DESCRIPTION:Title: Ra
ndom matrix models arising from projections of orbital measures\nby Co
lin McSwiggen (NYU) as part of Probability and the City Seminar\n\n\nAbstr
act\nA number of widely studied random matrix models can be realized as pr
ojections of invariant measures on group orbits. Examples include the ran
domized Horn's problem\, the randomized Schur's problem\, and the orbital
corners process. In this talk we will introduce a general framework that
unifies these models in the case of coadjoint orbits of a compact Lie grou
p. We will present both recent and classical results that hold in this ge
neral setting\, and we will discuss applications to combinatorial represen
tation theory and quantum information theory. The talk will be accessible
to probabilists without a background in Lie theory or representation theo
ry. Results presented will include joint work with Jean-Bernard Zuber\, R
obert Coquereaux\, and Benoît Collins.\n
LOCATION:https://researchseminars.org/talk/PatC/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Kahn (Rutgers)
DTSTART:20220304T173000Z
DTEND:20220304T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/52
DESCRIPTION:Title: Li
near cover time is exponentially unlikely\nby Jeff Kahn (Rutgers) as p
art of Probability and the City Seminar\n\n\nAbstract\nProving a 2009 conj
ecture of Itai Benjamini\, we show:\n\nFor any $C$ there is $c > 0$ so tha
t for any simple random walk on an $n$-vertex graph $G$\, the probability
that the first $Cn$ steps of the walk see every vertex is less than $\\exp
[-cn]$.\n\nA first ingredient in the proof of this is a similar statement
for Markov chains in which all transition probabilities are less than a su
itable function of $C$.\n\nJoint with Quentin Dubroff.\n
LOCATION:https://researchseminars.org/talk/PatC/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma Bailey (CUNY)
DTSTART:20220128T173000Z
DTEND:20220128T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/53
DESCRIPTION:Title: La
rge deviations of Selberg’s central limit theorem\, and random matrix th
eory connections\nby Emma Bailey (CUNY) as part of Probability and the
City Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PatC/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Koralov (Maryland)
DTSTART:20220204T173000Z
DTEND:20220204T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/54
DESCRIPTION:Title: Pe
rturbations of Parabolic Equations and Diffusion Processes with Degenerati
on: Boundary Problems and Metastability\nby Leonid Koralov (Maryland)
as part of Probability and the City Seminar\n\n\nAbstract\nWe study diffus
ion processes in a bounded domain with absorbing or reflecting boundary. T
he generator of the process is assumed to contain two terms: the main term
that degenerates on the boundary in a direction orthogonal to the boundar
y and a small non-degenerate perturbation. Understanding the behavior of s
uch processes allows us to study the stabilization of solutions to the cor
responding parabolic equations with a small parameter. Metastability effec
ts arise in this case: the asymptotics of solutions\, as the size of the p
erturbation tends to zero\, depends on the time scale. Initial-boundary va
lue problems with both the Dirichet and the Neumann boundary conditions wi
ll be considered. The talk is based on joint work with M. Freidlin.\n
LOCATION:https://researchseminars.org/talk/PatC/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximilian Nitzscher (NYU Courant)
DTSTART:20220211T173000Z
DTEND:20220211T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/55
DESCRIPTION:Title: Ph
ase transition for level-set percolation of the membrane model\nby Max
imilian Nitzscher (NYU Courant) as part of Probability and the City Semina
r\n\n\nAbstract\nWe consider level-set percolation for the Gaussian membra
ne model on the integer lattice in dimensions five and higher\, and establ
ish that as h varies\, a non-trivial percolation phase transition for the
level-set above level h occurs at some finite critical level\, which we sh
ow to be positive in high dimensions. Moreover\, we demonstrate the existe
nce of a strongly subcritical phase\, in which we provide bounds for the c
onnectivity function of the level-set above h\, and a strongly supercritic
al phase\, in which we characterize the geometry of the level-set above le
vel h. As a main tool\, we present novel decoupling inequalities for the m
embrane model\, which are instrumental in the study of both the subcritica
l and supercritical phases of its level-sets. This talk is based on joint
work with Alberto Chiarini.\n
LOCATION:https://researchseminars.org/talk/PatC/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Berestycki (Oxford)
DTSTART:20220218T173000Z
DTEND:20220218T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/56
DESCRIPTION:Title: Th
e extremal point process of branching Brownian motion in $\\R^d$\nby J
ulien Berestycki (Oxford) as part of Probability and the City Seminar\n\n\
nAbstract\nConsider a branching Brownian motion in $\\R^d$ with $d \\geq 1
$. Where are the particles that have traveled the furthest away from the o
rigin (at a large time $t$)? If one conditions by what happened early on i
n the process\, in which direction are we likely to fond the furthest part
icle? Can one describe the structure of the extremal point process at larg
e times? Those questions were already well understood for the case $d=1$.
IN this talk I will present some recent results concerning the multidimens
ional case.\nBased on a joint work with Yujin H. Kim\, Eyal Lubetzky\, Bas
tien Mallein\, Ofer Zeitouni.\n
LOCATION:https://researchseminars.org/talk/PatC/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hutchcroft (Caltech)
DTSTART:20220225T173000Z
DTEND:20220225T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/57
DESCRIPTION:Title: Cr
itical percolation on the hierarchical lattice\nby Tom Hutchcroft (Cal
tech) as part of Probability and the City Seminar\n\n\nAbstract\nWe consid
er long-range percolation on the hierarchical lattice\, a highly symmetric
ultrametric space that serves as a toy model for the Euclidean lattice Z^
d. We will outline how to prove up-to-constants estimates on point-to-poin
t connection probabilities for the model at criticality and outline severa
l open problems regarding further critical exponents for the model.\n
LOCATION:https://researchseminars.org/talk/PatC/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Sidorova (University College London)
DTSTART:20220311T173000Z
DTEND:20220311T183000Z
DTSTAMP:20260422T212726Z
UID:PatC/58
DESCRIPTION:Title: Lo
calisation and delocalisation in the parabolic Anderson model\nby Nadi
a Sidorova (University College London) as part of Probability and the City
Seminar\n\n\nAbstract\nThe parabolic Anderson problem is the Cauchy probl
em for the heat equation on the integer lattice with random potential. It
describes the mean-field behaviour of a continuous-time branching random w
alk. It is well-known that\, unlike the standard heat equation\, the solut
ion of the parabolic Anderson model exhibits strong localisation. In parti
cular\, for a wide class of iid potentials it is localised at just one poi
nt. However\, in a partially symmetric parabolic Anderson model\, the one-
point localisation breaks down for heavy-tailed potentials and remains unc
hanged for light-tailed potentials\, exhibiting a range of phase transitio
ns.\n
LOCATION:https://researchseminars.org/talk/PatC/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-François Rodriguez (Imperial College London)
DTSTART:20220325T163000Z
DTEND:20220325T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/59
DESCRIPTION:Title: Cr
itical exponents for three-dimensional percolation models with long-range
dependence\nby Pierre-François Rodriguez (Imperial College London) as
part of Probability and the City Seminar\n\n\nAbstract\nWe will report on
recent progress regarding the near-critical behavior of certain statistic
al mechanics models in dimension three. Our results deal with the phase tr
ansition associated to two percolation problems involving the Gaussian fre
e field (GFF) in 3D. In one case\, they determine a unique “fixed point
” corresponding to the transition\, which is proved to obey Fisher’s s
caling law. This is one of several relations classically conjectured by ph
ysicists to hold on the grounds of a corresponding scaling ansatz.\n
LOCATION:https://researchseminars.org/talk/PatC/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Van Peski (MIT)
DTSTART:20220401T163000Z
DTEND:20220401T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/60
DESCRIPTION:Title: p-
adic random matrices and particle systems\nby Roger Van Peski (MIT) as
part of Probability and the City Seminar\n\n\nAbstract\nRandom p-adic mat
rices have been studied since the late 1980s as natural models for random
groups appearing in number theory and combinatorics. Recently it has also
become clear that the theory has close structural parallels with singular
values of complex random matrices\, bringing new techniques from integrabl
e probability and motivating new questions. After outlining this area (no
background in p-adic matrices will be assumed)\, I will discuss results on
the distribution of analogues of singular values for products of many ran
dom p-adic matrices. Both prelimit and limit objects exhibit much more spa
tial independence than their analogues for complex matrices\, often with s
urprising results. In different regimes we can prove Gaussian limits\, an
intriguing new discrete Poisson-type local limit (yielding a local interac
ting particle system on $\\mathbb{Z}$ similar to $q$-TASEP)\, and converge
nce of global bulk fluctuations to a certain explicit Gaussian process.\n
LOCATION:https://researchseminars.org/talk/PatC/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Salez (Université Paris-Dauphine & PSL)
DTSTART:20220408T163000Z
DTEND:20220408T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/61
DESCRIPTION:by Justin Salez (Université Paris-Dauphine & PSL) as part of
Probability and the City Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PatC/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Dunlap (NYU Courant)
DTSTART:20220415T163000Z
DTEND:20220415T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/62
DESCRIPTION:Title: No
nlinear weak-noise stochastic heat equations in two dimensions\nby Ale
x Dunlap (NYU Courant) as part of Probability and the City Seminar\n\n\nAb
stract\nI will discuss a two-dimensional stochastic heat equation in the w
eak noise regime with a nonlinear noise strength. I will explain how point
wise statistics of solutions to this equation\, as the correlation length
of the noise is taken to 0 but the noise is attenuated by a logarithmic fa
ctor\, can be related to a forward-backward stochastic differential equati
on (FBSDE) depending on the nonlinearity. I will also discuss two cases in
which the FBSDE can be explicitly solved: the linear stochastic heat equa
tion\, for which we recover the log-normal behavior proved by Caravenna\,
Sun\, and Zygouras\, and branching Brownian motion/super-Brownian motion\,
for which we obtain a solution to the Feller diffusion. This talk will be
based on joint work with Yu Gu and with Cole Graham.\n
LOCATION:https://researchseminars.org/talk/PatC/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hubert Lacoin (IMPA)
DTSTART:20220422T163000Z
DTEND:20220422T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/63
DESCRIPTION:by Hubert Lacoin (IMPA) as part of Probability and the City Se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PatC/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Tassion (ETH Zurich)
DTSTART:20220429T163000Z
DTEND:20220429T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/64
DESCRIPTION:by Vincent Tassion (ETH Zurich) as part of Probability and the
City Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PatC/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Das (Columbia)
DTSTART:20220506T163000Z
DTEND:20220506T173000Z
DTSTAMP:20260422T212726Z
UID:PatC/65
DESCRIPTION:Title: Pa
th properties of the KPZ Equation and related polymers\nby Sayan Das (
Columbia) as part of Probability and the City Seminar\n\n\nAbstract\nThe K
PZ equation is a fundamental stochastic PDE that can be viewed as the log-
partition function of continuum directed random polymer (CDRP). In this ta
lk\, we will first focus on the fractal properties of the tall peaks of th
e KPZ equation. This is based on separate joint works with Li-Cheng Tsai a
nd Promit Ghosal. In the second part of the talk\, we will study the KPZ e
quation through the lens of polymers. In particular\, we will discuss loca
lization aspects of CDRP that will shed light on certain properties of the
KPZ equation such as ergodicity and limiting Bessel behaviors around the
maximum. This is based on joint work with Weitao Zhu.\n
LOCATION:https://researchseminars.org/talk/PatC/65/
END:VEVENT
END:VCALENDAR