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BEGIN:VEVENT
SUMMARY:Rick Kenyon (Yale)
DTSTART:20200417T170000Z
DTEND:20200417T180000Z
DTSTAMP:20260404T095118Z
UID:PatC/1
DESCRIPTION:Title: Gradient models and kappa-harmonic functions\nby Rick Kenyon (Yale
) as part of Probability and the City Seminar\n\n\nAbstract\nThis is joint
work with Istvan Prause. \nWe discuss random height models h:R^2 -> R and
their associated limit shapes. A gradient model is one whose surface tens
ion only depends on slope. Examples include the 6- and 8-vertex model and
FK-percolation models\, among many others. We show that limit shapes for s
uch a model can be explicitly parameterized using kappa-harmonic functions
\, that is\, solutions to the laplacian equation with spatially varying co
nductance kappa=kappa(x\,y). Here kappa is the square root of the Hessian
determinant of the surface tension.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remi Rhodes (Aix-Marseille)
DTSTART:20200424T150000Z
DTEND:20200424T160000Z
DTSTAMP:20260404T095118Z
UID:PatC/2
DESCRIPTION:Title: Conformal Bootstrap in Liouville theory\nby Remi Rhodes (Aix-Marse
ille) as part of Probability and the City Seminar\n\n\nAbstract\nLiouville
conformal field theory (denoted LCFT) is a 2-dimensional conformal field
theory depending on a parameter $\\gamma\\in\\R$ and studied since the eig
hties in theoretical physics. In the case of the theory on the Riemann sph
ere\, physicists proposed closed formulae for the n-point correlation func
tions using symmetries and representation theory\, called the DOZZ formula
(when n=3) and the conformal bootstrap (for n>3). A probabilistic constru
ction of LCFT was recently proposed by David-Kupiainen-Rhodes-Vargas for $
\\gamma \\in (0\,2]$ and the last three authors later proved the DOZZ form
ula. In this talk I will present a proof of equivalence between the probab
ilistic and the bootstrap construction (proposed in physics) for the n poi
nt correlation functions with n greater or equal to 4\, valid for $\\gamma
\\in (0\,1)$. Our proof combines the analysis of a natural semi-group\, to
ols from 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://stable.researchseminars.org/talk/PatC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Alexander (USC)
DTSTART:20200501T160000Z
DTEND:20200501T170000Z
DTSTAMP:20260404T095118Z
UID:PatC/3
DESCRIPTION:Title: Geodesics\, bigeodesics\, and coalescence in first passage percolation
in general dimension\nby Ken Alexander (USC) as part of Probability a
nd the City Seminar\n\n\nAbstract\nIn first passage percolation (FPP) on $
\\mathbb{Z}^d$\, i.i.d.~(bond) passage times are attached to the nearest-n
eighbor bonds of the lattice\, and the passage time from $x$ to $y$ is the
shortest sum of bond passage times among all possible paths from $x$ to $
y$\; the corresponding minimizing path is called a geodesic. One can also
consider geodesic rays and bigeodesics\, which are one-ended and two-ended
infinite paths for which every finite segment is a geodesic\; a $\\theta$
-ray is a geodesic ray with asymptotic direction $\\theta$. The conjecture
d picture\, partly verified for $d=2$ under assumptions of various strengt
hs\, is that for a given $\\theta$\, there is a.s.~a unique $\\theta$--ray
from each lattice site\, and any two $\\theta$--rays eventually coalesce\
, though there is a random null set of directions for which this fails\; b
igeodesics a.s.~do not exist at all. Here we establish portions of this he
uristic picture in higher dimensions (where few results currently exist)\,
at least under the assumption that certain very basic but unproven proper
ties of FPP are valid. We establish a coalescence-like property: taking al
l the $\\theta$--rays starting next to a given hyperplane\, and looking at
the set of points where they cross another hyperplane some distance $r$ a
head of the starting one\, we show that the geodesics bundle together in t
he sense that the density of the crossing points approaches 0 (at a near-s
harp rate) as $r\\to\\infty$. This bundling property also holds if we cons
ider together all $\\theta$--rays over a narrow range of directions $\\the
ta$\, and this fact leads to proof of the absence of bigeodesics. In $d=2$
\, bundling can be used to bound the probability that two $\\theta$--rays
do not coalesce before traveling a distance $r$.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dima Ioffe (Technion)
DTSTART:20200508T140000Z
DTEND:20200508T150000Z
DTSTAMP:20260404T095118Z
UID:PatC/4
DESCRIPTION:Title: Uphill diffusions via phase transitions.\nby Dima Ioffe (Technion)
as part of Probability and the City Seminar\n\n\nAbstract\nUphill diffusi
ons is an umbrella name for a variety of phenomena when stationary particl
e current goes from low density to high density\, in an ostensible violati
on of Fick's first law. In this talk I shall present an ongoing joint proj
ect with Anna De Masi\, Titti Merola and Errico Presutti\, where uphill di
ffusions are uncovered and described in the context of two dimensional sto
chastic phase-field models - a dynamically coupled Ginsburg Landau model a
nd Ising model in the phase transition regime.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Sly (Princeton)
DTSTART:20200515T150000Z
DTEND:20200515T160000Z
DTSTAMP:20260404T095118Z
UID:PatC/5
DESCRIPTION:Title: Critical One-dimensional Multi-particle DLA\nby Allan Sly (Princet
on) as part of Probability and the City Seminar\n\n\nAbstract\nIn multi-pa
rticle Diffusion Limited Aggregation (DLA) a sea of particles perform inde
pendent random walks until they run into the aggregate and are absorbed.
In dimension 1\, the rate of growth of the aggregate depends on lambda\,
the density of the particles. Kesten and Sidoravicius proved that when $\
\lambda <1$ the aggregate grows like $t^{1/2}$. They furthermore predicte
d linear growth when $\\lambda > 1$ (subsequently confirmed) and $t^{2/3}$
growth at the critical density $\\lambda =1$. \n\nIn this talk we address
the critical case\, confirming the $t^{2/3}$ rate of growth and show that
aggregate has a scaling limit whose derivative is a self-similar diffusio
n process. Surprisingly this contradicts conjectures on the speed in the
mildly supercritical regime when $\\lambda = 1 + \\epsilon$.\n\nJoint work
with Danny Nam and Dor Elboim\n
LOCATION:https://stable.researchseminars.org/talk/PatC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Sheffield (MIT)
DTSTART:20200529T150000Z
DTEND:20200529T160000Z
DTSTAMP:20260404T095118Z
UID:PatC/6
DESCRIPTION:Title: Probability and pandemics\nby Scott Sheffield (MIT) as part of Pro
bability and the City Seminar\n\n\nAbstract\nIn one of the simplest epidem
ic models\, one lets $p_n$ denote the number of new infections during week
$n$ and 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 ta
kes place between people during the nth week. Within this simplistic model
\, intermittent strategies (taking $c_n$ small some weeks and large other
weeks) lead to lower infection rates than consistent strategies with the s
ame total amount of contact.\n\nBut what happens if one considers a more r
ealistic disease model (such as a SEIR model with multiple compartments\,
or a network-based model\, with empirically based distributions for incuba
tion and infection times) and also tries to assign utility to the amount o
f contact in a more realistic way (accounting for crowding\, social networ
king and other issues)? What factors cause intermittent strategies to outp
erform constant strategies? I will discuss a health policy paper I recentl
y co-authored with a team of public health researchers that explores this
question for a range of simple examples.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reza Gheissari (U.C. Berkeley)
DTSTART:20200619T170000Z
DTEND:20200619T180000Z
DTSTAMP:20260404T095118Z
UID:PatC/7
DESCRIPTION:Title: Cube-root fluctuations and Tracy--Widom tails in critically pre-wetted
Ising interfaces\nby Reza Gheissari (U.C. Berkeley) as part of Probab
ility and the City Seminar\n\n\nAbstract\nConsider the 2D Ising model at l
ow temperature on an $N\\times N$ box with minus boundary conditions on th
e bottom and plus boundary conditions on the other three sides\, in the pr
esence 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 confined by the interface is $N^{\\frac{4}{3}+o(1)}$. Since then mor
e refined features of such interfaces---which have been conjectured to con
verge to the Ferrari--Spohn diffusion in critically sized $N^{2/3}\\times
N^{1/3}$ windows--- have only been proven for approximations given by rand
om walks under area tilts. \n\nI will discuss recent work with Shirshendu
Ganguly obtaining a more refined understanding of the local and global geo
metry of the Ising interface in the critical pre-wetting regime. As part o
f 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://stable.researchseminars.org/talk/PatC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Toninelli (Vienna)
DTSTART:20200626T140000Z
DTEND:20200626T150000Z
DTSTAMP:20260404T095118Z
UID:PatC/8
DESCRIPTION:Title: The stationary (2+1)-dimensional AKPZ equation\nby Fabio Toninelli
(Vienna) as part of Probability and the City Seminar\n\n\nAbstract\nThe A
KPZ equation is an anisotropic variant of the celebrated (two-dimensional)
KPZ stochastic PDE\, which is expected to describe the large-scale behavi
or of (2+1)-dimensional growth models whose average speed of growth is a n
on-convex function of the average slope (AKPZ universality class). Several
interacting particle systems belonging to the AKPZ class are known\, nota
bly a class of two-dimensional interlaced particle systems introduced by A
. Borodin and P. Ferrari.\n\nIn the physics literature\, the AKPZ equation
was conjectured to have the same large-scale behavior as the stochastic h
eat equation with additive noise (2d-SHE). In this talk\, I will show that
this is not really true: in fact\, the stationary equation is not invaria
nt under diffusive rescaling (as the 2d-SHE is)\, not even asymptotically
on large scales\, and logarithmic corrections in the scaling are needed in
stead. [Based on joint work with G. Cannizzaro and D. Erhard]\n
LOCATION:https://stable.researchseminars.org/talk/PatC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Penington (Bath)
DTSTART:20201016T163000Z
DTEND:20201016T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/10
DESCRIPTION:Title: Brownian bees in the infinite swarm limit\nby Sarah Penington (Ba
th) 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 rate one. Each time a particle branches\, the particle in the system f
urthest 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://stable.researchseminars.org/talk/PatC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (Toronto)
DTSTART:20201023T163000Z
DTEND:20201023T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/11
DESCRIPTION:Title: Convergence of finite range exclusions and KPZ equation to the KPZ fi
xed point\nby Jeremy Quastel (Toronto) as part of Probability and the
City Seminar\n\n\nAbstract\nWe will describe a method of comparison with T
ASEP which proves that both the KPZ equation and finite range exclusion mo
dels converge to the KPZ fixed point. For the KPZ equation and the neares
t neighbour exclusion\, the initial data is allowed to be a continuous fun
ction plus a finite number of narrow wedges\, but for non-nearest neighbou
r exclusions\, one needs at the present time some randomization of the ini
tial data. We will give a little background\, but the talk will mostly be
about the proof. Joint work with Sourav Sarkar.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (Freie Universität Berlin)
DTSTART:20201030T163000Z
DTEND:20201030T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/12
DESCRIPTION:Title: Mass 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 behavior of the total mass of the 2d parabolic Anderson model (PAM) w
ith white noise potential\, which is the universal scaling limit of 2d bra
nching random walks in small random environments. There are several known
results on the long time behavior of the PAM for more regular potentials\,
but the 2d white noise is very singular and it requires renormalization t
echniques. In particular\, the Feynman-Kac representation\, usually the ma
in tool for deriving asymptotics\, breaks down. To overcome this problem w
e use a measure transform and we introduce a new "partial Feynman-Kac repr
esentation“. The new representation is based on a diffusion with distrib
utional drift\, and we derive Gaussian heat kernel bounds for such diffusi
ons. Based on joint works with Wolfgang König and Willem van Zuijlen.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (NYU Courant)
DTSTART:20201204T173000Z
DTEND:20201204T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/13
DESCRIPTION:Title: Microscopic description of Coulomb gases\nby Sylvia Serfaty (NYU
Courant) as part of Probability and the City Seminar\n\n\nAbstract\nWe are
interested in the statistical mechanics of systems of N points with Coulo
mb interactions in general dimension for a broad temperature range.\nWe di
scuss local laws characterizing the rigidity of the system at the microsco
pic level\, as well as free energy expansion and Central Limit Theorems fo
r fluctuations.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Damron (Georgia Tech)
DTSTART:20201211T173000Z
DTEND:20201211T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/14
DESCRIPTION:Title: Critical first-passage percolation in two dimensions\nby Michael
Damron (Georgia Tech) as part of Probability and the City Seminar\n\n\nAbs
tract\nIn 2d first-passage percolation (FPP)\, we place nonnegative i.i.d.
weights (t_e) on the edges of Z^2 and study the induced weighted graph ps
eudometric T = T(x\,y) If we denote by p = P(t_e = 0)\, then there is a tr
ansition 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 sto
chastically 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 distrib
ution function of t_e near zero. I will discuss my work over the past few
years that (a) determines the exact rate of growth of T(0\,x)\, (b) determ
ines the "time constant" for the site-FPP model on the triangular lattice
and\, more recently (c) studies the growth of T(0\,x) in a dynamical versi
on of the model\, where weights are resampled according to independent exp
onential clocks. These are joint works with J. Hanson\, D. Harper\, W.-K.
Lam\, P. Tang\, and X. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-François Le Gall (Paris-Saclay)
DTSTART:20201106T173000Z
DTEND:20201106T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/20
DESCRIPTION:Title: Compact and non-compact models of random geometry\nby Jean-Franç
ois Le Gall (Paris-Saclay) as part of Probability and the City Seminar\n\n
\nAbstract\nWe discuss various models of random geometry that arise as sca
ling limits of large planar graphs embedded in the 2-sphere (also called
planar maps). The most popular compact models are the Brownian sph
ere or Brownian map\, and the Brownian disk\, which is the scaling
limit of planar maps with a boundary. We explain how Brownian disks
can be viewed as connected components of the complement of balls in th
e Brownian sphere\, and we discuss a remarkable growth-fragmentation pr
ocess that describes the evolution of the boundary sizes of these co
mponents when the radius of the ball increases. We also introduce the n
on-compact models called the Brownian plane\, the infinite Brownian
disk and the Brownian half-plane\, and we present a unified construc
tion of these three models based on a spine decomposition. Most of
the talk is based on joint work with Armand Riera.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhan Aru (EPFL Lausanne)
DTSTART:20201113T173000Z
DTEND:20201113T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/21
DESCRIPTION:Title: Imaginary multiplicative chaos: different questions from different co
ntexts\, and a few answers too\nby Juhan Aru (EPFL Lausanne) as part o
f Probability 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 ex
ample\n- as a analytic continuation of the real multiplicative chaos\, tha
t is central in the probabilistic study of Liouville quantum gravity and L
iouville CFT\;\n- when taking the continuum limit of the spin field for th
e XOR-Ising model\;\n- in relation to the Kosterlitz-Thouless-type of phas
e transitions.\nIn this talk I will try to explain how imaginary chaos com
es up in these contexts\, which questions it brings along\, and how to ans
wer some of these questions. \nThis is a joint work with J. Junnila\, and
also partly with A. Jego.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Ahn (MIT)
DTSTART:20201002T163000Z
DTEND:20201002T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/22
DESCRIPTION:by Andrew Ahn (MIT) as part of Probability and the City Semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PatC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Kosygina (Baruch College and the CUNY Graduate Center)
DTSTART:20210402T163000Z
DTEND:20210402T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/23
DESCRIPTION:Title: From generalized Ray-Knight theorems to functional CLTs for some mode
ls of self-interacting random walks on Z\nby Elena Kosygina (Baruch Co
llege and the CUNY Graduate Center) as part of Probability and the City Se
minar\n\n\nAbstract\nIn several models of self-interacting random walks (S
IRWs) on Z generalized Ray-Knight theorems for local times proved to be a
very useful tool for studying the limiting behavior of these walks. Exampl
es include some reinforced random walks\, asymptotically free and polynomi
ally self-repelling random walks\, excited random walks\, rotor walks with
defects. I shall give an overview of some of these models and then concen
trate on the joint work with Thomas Mountford (EPFL) and Jon Peterson (Pur
due University) on the functional limit theorem for recurrent excited rand
om walks with Markovian cookie stacks.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Cook (Duke)
DTSTART:20210122T173000Z
DTEND:20210122T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/24
DESCRIPTION:Title: Universality for the minimum modulus of random trigonometric polynomi
als\nby Nick Cook (Duke) as part of Probability and the City Seminar\n
\n\nAbstract\nWe consider the restriction to the unit circle of random deg
ree-n polynomials with iid normalized coefficients (Kac polynomials). Rece
nt work of Yakir and Zeitouni shows that for Gaussian coefficients\, the m
inimum modulus (suitably rescaled) follows a limiting exponential distribu
tion. We show this is a universal phenomenon\, extending their result to a
rbitrary sub-Gaussian coefficients\, such as Rademacher signs. For discret
e distributions we must now deal with possible arithmetic structure in the
polynomial evaluated at different points of the circle. On "minor arcs" w
e obtain strong comparisons with the Gaussian model by translating to a ra
ndom walk in a high dimensional phase space\, and obtaining strong decay e
stimates on characteristic functions\, while major arcs can be handled wit
h cruder arguments. Based on joint work with Hoi Nguyen.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Pain (NYU Courant)
DTSTART:20210129T173000Z
DTEND:20210129T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/25
DESCRIPTION:Title: Optimal local law and central limit theorem for beta-ensembles\nb
y Michel Pain (NYU Courant) as part of Probability and the City Seminar\n\
n\nAbstract\nIn this talk\, I will present a joint work with Paul Bourgade
and Krishnan Mody. We consider beta-ensembles with general potentials (or
equivalently a log-gas in dimension 1)\, which are a generalization of Ga
ussian beta-ensembles and of classical invariant ensembles of random matri
ces. We prove a multivariate central limit theorem for the logarithm of th
e characteristic polynomial\, showing that it behaves as a log-correlated
field. A key ingredient is an optimally sharp local law for the the Stielj
es transform of the empirical measure which can be of independent interest
. Both the proofs of the CLT and the local law are based essentially on lo
op equations techniques.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Garban (Lyon)
DTSTART:20210205T173000Z
DTEND:20210205T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/26
DESCRIPTION:Title: Vortex fluctuations in continuous spin systems and lattice gauge theo
ry\nby Christophe Garban (Lyon) as part of Probability and the City Se
minar\n\n\nAbstract\nTopological phase transitions were discovered by Bere
zinskii-Kosterlitz-Thouless (BKT) in the 70's. They describe intriguing ph
ase transitions 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 Co
ulomb gas\n\n - the integer-valued Gaussian Free Field (or Z-ferromagnet)\
n\n - Abelian lattice gauge theory on Z^4\n\nIn this talk\, I will explain
a new technique to obtain quantitative lower bounds on the fluctuations i
nduced by the topological defects (vortices) on such systems at low temper
ature. We will see in particular that the fluctuations generated by the vo
rtices 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
matching lower bounds with the fluctuations predicted from RG analysis. I
will start the talk by giving an overview of the above models. The talk is
based on joint works with Avelio Sepúlveda.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Shen (Wisconsin)
DTSTART:20210212T173000Z
DTEND:20210212T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/27
DESCRIPTION:Title: Stochastic quantization\, large N\, and mean field limit\nby Hao
Shen (Wisconsin) as part of Probability and the City Seminar\n\n\nAbstract
\nWe study "large N problems” in quantum field theory using SPDE methods
via stochastic quantization. In the SPDE setting this is formulated as me
an field problems. We will consider the vector Phi^4 model (i.e. linear si
gma model)\, whose stochastic quantization is a system of N coupled dynami
cal Phi^4 SPDEs. We discuss a series of results. First\, in 2D\, we prove
mean field limit for these dynamics as N goes to infinity. We also show th
at the quantum field theory converges to massive Gaussian free field in th
is limit\, in both 2D and 3D. Moreover we prove exact formulae for some co
rrelations of O(N)-invariant observables in the large N limit\; such formu
lae were predicted using “bubble diagrams” in physics.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Hammond (UC Berkeley)
DTSTART:20210312T173000Z
DTEND:20210312T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/29
DESCRIPTION:Title: Stability and chaos in dynamical last passage percolation\nby Ala
n Hammond (UC Berkeley) as part of Probability and the City Seminar\n\n\nA
bstract\nMany complex statistical mechanical models have intricate energy
landscapes. The ground state\, or lowest energy state\, lies at the base o
f the deepest valley. In examples such as spin glasses and Gaussian polyme
rs\, there are many valleys\; the abundance of near-ground states (at the
base of valleys) indicates the phenomenon of chaos\, under which the groun
d state alters profoundly when the model's disorder is slightly perturbed.
Indeed\, a monograph of Sourav Chatterjee from 2014 establishes that\, fo
r a class of models of Gaussian disorder\, this abundance of competing min
imizers is accompanied both by a rapid outset of chaos under perturbation
of the system by noise\, and by the effect of super-concentration\, in wh
ich model statistics have lower variance than in classical scenarios\, for
which a central limit theorem may apply.\n\nIn this talk\, a recent inves
tigation\, jointly undertaken with Shirshendu Ganguly\, of a natural dynam
ics for a model of planar last passage percolation will be discussed. Robu
st probabilistic and geometric technique permits a very quantified analysi
s of the presence of close rivals in energy to the ground state for the st
atic version of the model\; consequently\, the order of the scale that her
alds the transition from stability to chaos for the dynamical model is ide
ntified. The tools that drive the investigation include harmonic analytic
technique present in Chatterjee's work\, and the use of Brownian Gibbs res
ampling analysis for random ensembles of curves naturally associated to la
st passage percolation via the Robinson-Schensted-Knuth correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Maas (IST Austria)
DTSTART:20210319T163000Z
DTEND:20210319T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/30
DESCRIPTION:Title: Homogenisation of discrete dynamical optimal transport\nby Jan Ma
as (IST Austria) as part of Probability and the City Seminar\n\n\nAbstract
\nMany stochastic systems can be viewed as gradient flow ('steepest descen
t') in the space of probability measures\, where the driving functional is
a relative entropy and the relevant geometry is described by a dynamical
optimal transport problem. In this talk we focus on these optimal transpor
t problems and describe recent work on the limit passage from discrete to
continuous.\n\nSurprisingly\, it turns out that discrete transport metrics
may fail to converge to the expected limit\, even when the associated gra
dient flows converge. We will illustrate this phenomenon in examples and p
resent a recent homogenisation result.\n\nThis talk is based on joint work
with Peter Gladbach\, Eva Kopfer\, and Lorenzo Portinale.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bufetov (Bonn)
DTSTART:20210219T173000Z
DTEND:20210219T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/31
DESCRIPTION:Title: Cutoff profile of ASEP on a segment\nby Alexey Bufetov (Bonn) as
part of Probability and the City Seminar\n\n\nAbstract\nThe mixing behavio
r of the Asymmetric Simple Exclusion Process (=ASEP) on a segment will be
discussed. We will show that its cutoff profile is given by the Tracy-Wido
m distribution function\, which extends earlier results of Labbe-Lacoin an
d Benjamini-Berger-Hoffman-Mossel. We will also discuss a multi-species ve
rsion of this model (also known as a biased card shuffling or an oriented
swap process). The talk is based on joint works with P. Nejjar and with V.
Gorin\, D. Romik.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveliina Peltola (Bonn)
DTSTART:20210305T173000Z
DTEND:20210305T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/32
DESCRIPTION:Title: On large deviations of SLEs\, real rational functions\, and zeta-regu
larized determinants of Laplacians\nby Eveliina Peltola (Bonn) as part
of Probability and the City Seminar\n\n\nAbstract\nThe talk concerns a la
rge deviation principle (LDP) for (multiple) Schramm-Loewner evolution (SL
E) curves for the Hausdorff metric.\nWhen studying the LDP\, we introduced
a ''Loewner potential'' that describes the rate function.\nThis object tu
rned out to have several intrinsic\, and perhaps surprising\, connections
to various fields.\nFor instance\, it has a simple expression in terms of
zeta-regularized determinants of Laplace-Beltrami operators.\nOn the other
hand\, minima of the Loewner potential solve a nonlinear first order PDE
that arises\nin a semiclassical limit of certain correlation functions in
conformal field theory (arguably also related to isomonodromic systems).\n
Finally\, the Loewner potential minimizers classify rational functions wit
h real critical points\, thereby providing a novel proof for\na version of
the now well-known Shapiro-Shapiro conjecture in real enumerative geometr
y. This talk is based on joint work with Yilin Wang (MIT).\n
LOCATION:https://stable.researchseminars.org/talk/PatC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Bodineau (École Polytechnique)
DTSTART:20210409T163000Z
DTEND:20210409T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/33
DESCRIPTION:Title: Fluctuating Boltzmann equation and large deviations for a hard sphere
gas\nby Thierry Bodineau (École Polytechnique) as part of Probabilit
y and the City Seminar\n\n\nAbstract\nA gas dynamics can be modelled by a
billiard made of hard spheres\, moving according to the laws of classical
mechanics. Initially the spheres are randomly distributed according to a p
robability measure which is then transported by the flow of the determinis
tic dynamics. Since the seminal work of Lanford\, it is known in the kinet
ic limit 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 f
luctuations of the microscopic dynamics around the Boltzmann equation and
the convergence of the fluctuation field to the fluctuating Boltzmann equa
tion. We will also show that the occurence of atypical evolutions can be q
uantified by a large deviation principle. This analysis relies on the stud
y of the correlations created by the Hamiltonian dynamics. We will see tha
t the emergence of irreversibility in the kinetic limit can be related to
the singularity of these correlations.\n\nZoom meeting ID: 991 4448 8133\,
password: 800920\n
LOCATION:https://stable.researchseminars.org/talk/PatC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Angel (UBC)
DTSTART:20210326T163000Z
DTEND:20210326T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/34
DESCRIPTION:Title: A tale of two balloons\nby Omer Angel (UBC) as part of Probabilit
y and the City Seminar\n\n\nAbstract\nWe study the following process\, mot
ivated by coalescing random\nwalks: From each point of a Poisson point pro
cess start growing a\nballoon at rate 1. When two balloons touch\, they po
p and disappear. We\nstudy this on various spaces and various starting sta
tes. En route we\nfind a new(ish) 0-1 law\, and generalize bounds on indep
endent sets that\nare factors of IID. Joint work with Gourab Ray and Yinon
Spinka.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Dauvergne (Princeton)
DTSTART:20210226T173000Z
DTEND:20210226T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/35
DESCRIPTION:Title: Learning from the directed landscape\nby Duncan Dauvergne (Prince
ton) as part of Probability and the City Seminar\n\n\nAbstract\nThe direct
ed landscape is a random `directed metric' on the \nspacetime plane that a
rises as the scaling limit of integrable models \nof last passage percolat
ion. 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 desc
ribe its construction in terms of the \nAiry line ensemble\, give an exten
sion of this construction for optimal \nlength disjoint paths in the direc
ted landscape\, and show how these \nconstructions reveal surprising Brown
ian structures in the directed \nlandscape. Based on joint work with J. Or
tmann\, B. Virag\, and L. Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Wu (NYU Shanghai)
DTSTART:20210416T140000Z
DTEND:20210416T150000Z
DTSTAMP:20260404T095118Z
UID:PatC/36
DESCRIPTION:Title: Massless phases for the Villain model in d>=3\nby Wei Wu (NYU Sha
nghai) as part of Probability and the City Seminar\n\n\nAbstract\nThe XY a
nd the Villain models are mathematical idealization of real world models o
f liquid crystal\, liquid helium\, and superconductors. Their phase transi
tion has important applications in condensed matter physics and led to th
e Nobel Prize in Physics in 2016. However we are still far from a complete
mathematical understanding of the transition. The spin wave conjecture\,
originally proposed by Dyson and by Mermin and Wagner\, predicts that at l
ow temperature\, large scale behaviors of these models are closely related
to Gaussian free fields. I will review the historical background and dis
cuss some recent progress on this conjecture in d>=3. Based on the joint w
ork with Paul Dario (Tel Aviv).\n
LOCATION:https://stable.researchseminars.org/talk/PatC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeni Dimitrov (Columbia)
DTSTART:20210423T163000Z
DTEND:20210423T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/37
DESCRIPTION:Title: Towards universality for Gibbsian line ensembles\nby Evgeni Dimit
rov (Columbia) as part of Probability and the City Seminar\n\n\nAbstract\n
Gibbsian line ensembles are natural objects that arise in statistical mech
anics models of random tilings\, directed polymers\, random plane partitio
ns and avoiding random walks. In this talk I will discuss a general framew
ork for establishing universal KPZ scaling limits for sequences of Gibbsia
n line ensembles. This framework is still being developed and I will expla
in some of the recent progress that has been made towards carrying it our
for two integrable models of random Hall-Littlewood plane partitions and l
og-gamma polymers.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Matetski (Columbia)
DTSTART:20210514T163000Z
DTEND:20210514T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/38
DESCRIPTION:Title: Directed mean curvature flow in noisy environment\nby Konstantin
Matetski (Columbia) as part of Probability and the City Seminar\n\n\nAbstr
act\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 quenched KPZ equation with a weak noise. We prove that\, when started
from a sufficiently regular initial state\, a rescaled and renormalized c
urve converges to the Cole–Hopf solution of the KPZ equation. This is a
joint work with A.Gerasimovičs and M. Hairer.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cannizzaro (Warwick)
DTSTART:20210521T163000Z
DTEND:20210521T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/39
DESCRIPTION:Title: Edwards-Wilkinson fluctuations for the Anisotropic KPZ in the weak co
upling regime\nby Giuseppe Cannizzaro (Warwick) as part of Probability
and the City Seminar\n\n\nAbstract\nIn this talk\, we present recent resu
lts on an anisotropic variant of the Kardar-Parisi-Zhang equation\, the An
isotropic KPZ equation (AKPZ)\, in the critical spatial dimension d=2. Thi
s is a singular SPDE which is conjectured to capture the behaviour of the
fluctuations of a large family of random surface growth phenomena but whos
e analysis falls outside of the scope not only of classical stochastic cal
culus but also of the theory of Regularity Structures and paracontrolled c
alculus. We first prove the conjecture made in [Cannizzaro\, Erhard\, Toni
nelli\, "The AKPZ equation at stationarity: logarithmic superdiffusivity"]
\, i.e. we show that the nonlinearity causes a logarithmically superdiffus
ive behaviour at large scales and more precisely that correlation length o
f the solution grows like t1/2 (log t)1/4 up to lower order correction. Mo
tivated by the previous\, we consider the AKPZ equation in the so-called w
eak coupling regime\, i.e. the equation regularised at scale N and the coe
fficient of the nonlinearity tuned down by a factor (log N)-1/2\, and prov
e that\, for N going to infinity\, its solution converges to a linear stoc
hastic heat equation with renormalised coefficients.\nThe talk is based on
(ongoing) joint work with D. Erhard and F. Toninelli.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Gu (Carnegie Mellon University)
DTSTART:20210430T163000Z
DTEND:20210430T173000Z
DTSTAMP:20260404T095118Z
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 j
oint work with Tomasz Komorowski on proving Gaussian fluctuations for the
KPZ equation on the torus.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramon van Handel (Princeton)
DTSTART:20210917T163000Z
DTEND:20210917T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/41
DESCRIPTION:Title: Sharp matrix concentration inequalities\nby Ramon van Handel (Pri
nceton) as part of Probability and the City Seminar\n\n\nAbstract\nWhat do
es the spectrum of a random matrix look like when we make no\nassumption w
hatsoever about the covariance pattern of its entries? It may\nappear hop
eless that anything useful can be said at this level of\ngenerality. Nonet
heless\, a set of tools known as "matrix concentration\ninequalities" make
s it possible to estimate at least the spectral norm of\nvery general rand
om matrices up to logarithmic factors in the dimension.\nOn the other hand
\, it is well known that these inequalities fail to yield\nsharp results f
or even the simplest random matrix models.\n\nIn this talk I will describe
a powerful new class of matrix concentration\ninequalities that achieve o
ptimal results in many situations that are\noutside the reach of classical
methods. Our results are easily applicable\nin concrete examples\, and yi
eld detailed nonasymptotic information on the\nfull spectrum of essentiall
y arbitrarily structured random matrices. These\nnew inequalities arise fr
om an unexpected phenomenon: the spectrum of\nrandom matrices is accuratel
y captured by certain predictions of free\nprobability theory under surpri
singly minimal assumptions. Our proofs\nquantify the notion that it costs
little to be free.\n\nThe talk is based on joint works with Afonso Bandeir
a and March\nBoedihardjo\, and with Tatiana Brailovskaya. No prior backgro
und will be\nassumed.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Chatterjee (Stanford)
DTSTART:20211001T163000Z
DTEND:20211001T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/42
DESCRIPTION:Title: Local KPZ behavior under arbitrary scaling limits\nby Sourav Chat
terjee (Stanford) as part of Probability and the City Seminar\n\n\nAbstrac
t\nOne of the main difficulties in proving convergence of discrete models
of surface 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 limit is nontrivial\, is not known in a rigorous sense. The same probl
em has so far prevented the construction of nontrivial solutions of the KP
Z equation in dimensions higher than one. To understand KPZ growth without
being hindered by this issue\, I will introduce a new concept in this tal
k\, called "local KPZ behavior"\, which roughly means that the instantaneo
us growth 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 negligible compared to the other three terms and their sum. The main r
esult is that for a general class of surfaces\, which contains the model o
f directed polymers in a random environment as a special case\, local KPZ
behavior occurs under arbitrary scaling limits\, in any dimension.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Titus Lupu (CNRS and Sorbonne Université)
DTSTART:20210924T163000Z
DTEND:20210924T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/43
DESCRIPTION:Title: Multiplicative chaos of the 2D Brownian loop soup\nby Titus Lupu
(CNRS and Sorbonne Université) as part of Probability and the City Semina
r\n\n\nAbstract\nIt is known from the works in Mathematical Physics that t
he continuum Gaussian free field (GFF) admits representations in terms of
occupation measures of Brownian trajectories. In particular\, the square o
f the GFF (suitably renormalized) has the same distribution as the occupat
ion measure of a Poisson point process of Brownian loops\, known as the Br
ownian loop soup. This is the Le Jan's isomorphism theorem. The Brownian l
oop soups come with an intensity parameter $\\theta >0$\, and the connecti
on to the GFF is for the particular parameter $\\theta=1/2$. In our work w
e related the theory of the Gaussian Multiplicative Chaos (GMC) in 2D (ren
ormalized exponential of the 2D continuum GFF\, also appearing in Liouvill
e field theory) to the 2D Brownian loop soup. Actually we constructed a so
called multiplicative chaos of the Brownian loop soup for every intensity
parameter $\\theta$. Compared to the multiplicative chaos of a single 2D
Brownian trajectory\, which has been first constructed by Bass\, Burdzy an
d Khoshnevisan in the 90s\, in our work we require an additional layer of
renormalization due to ultraviolet divergence in the Brownian loop soup. F
or the particular parameter $\\theta=1/2$\, our multiplicative chaos of th
e Brownian loop soup has the same distribution as the renormalized hyperbo
lic cosine of the GFF\, i.e. is a sum of two GMCs. For other intensity par
ameters $\\theta$ we obtain new non-Gaussian multiplicative chaoses\, whic
h satisfy moreover a covariance property under conformal transformations o
f the domain. This is joint work with Elie Aïdekon (Sorbonne Université/
Fudan University)\, Nathanael Berestycki (University of Vienna) and Antoin
e Jégo (University of Vienna).\n
LOCATION:https://stable.researchseminars.org/talk/PatC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arjun Krishnan (Rochester)
DTSTART:20211015T163000Z
DTEND:20211015T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/44
DESCRIPTION:Title: Correlations of Busemann functions and the 2nd KPZ relationship\n
by Arjun Krishnan (Rochester) as part of Probability and the City Seminar\
n\n\nAbstract\nBusemann functions (correctors in homogenization theory) ar
e objects of interest in first- and last-passage percolation. Determining
the correlations of Busemann function increments is important because of i
ts relationship to the second KPZ relationship that relates the two fluctu
ation exponents in the models. We show that the correlations of adjacent B
usemann increments in last-passage percolation with general weights are di
rectly related to the time-constant of last-passage percolation with expon
ential weights (an integrable model). Using this relationship\, we give an
easily checkable condition that determines when adjacent Busemann increme
nts are negatively correlated\, and prove that\, for example\, last-passag
e percolation with iid Bernoulli weights has negatively correlated adjacen
t Busemann increments.\n\nJoint work with I. Alevy\n
LOCATION:https://stable.researchseminars.org/talk/PatC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morris Ang (MIT)
DTSTART:20211105T163000Z
DTEND:20211105T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/45
DESCRIPTION:Title: Integrability of the conformal loop ensemble\nby Morris Ang (MIT)
as part of Probability and the City Seminar\n\n\nAbstract\nFor 8/3 < κ <
8\, the conformal loop ensemble CLEκ is a canonical random ensemble of l
oops which is conformally invariant in law\, and whose loops locally look
like Schramm-Loewner evolution with parameter κ. It describes the scaling
limits of the Ising model\, percolation\, and other models. When κ ≤ 4
the loops are simple curves. In this regime we compute the three-point ne
sting statistic of CLEκ on the sphere\, and show it agrees with the imagi
nary DOZZ formula of Zamolodchikov (2005). We also obtain the expression
of the (properly normalized) probability that three points are on the same
CLE loop in terms of the DOZZ formula. The analogous quantity for three p
oints on the same cluster was previously conjectured by Delfino and Viti.
To our best knowledge our formula has not been predicted in the physics li
terature. Our arguments depend on couplings of CLE with Liouville quantum
gravity and the integrability of Liouville conformal field theory. Based
on joint work with Xin Sun.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Chiarini (Eindhoven University of Technology)
DTSTART:20211112T173000Z
DTEND:20211112T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/46
DESCRIPTION:Title: Disconnection and entropic repulsion for the harmonic crystal with ra
ndom conductances\nby Alberto Chiarini (Eindhoven University of Techno
logy) as part of Probability and the City Seminar\n\n\nAbstract\nWe study
level-set percolation of the discrete Gaussian free field on the Euclidean
lattice in three and more dimensions\, equipped with uniformly elliptic r
andom conductances. We prove that this percolation model undergoes a non-t
rivial 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 below a given level disconnects the discrete blow-up of A from the b
oundary of an enclosing box\, in a strongly percolative regime. We present
quenched asymptotic upper and lower bounds on this probability in terms o
f the homogenized capacity of A. The upper and lower bounds concerning dis
connection that we derive are plausibly matching at leading order. In this
case\, this work shows that conditioning on disconnection leads to an ent
ropic push-down of the field. (Based on a joint work with M. Nitzschner NY
U Courant)\n
LOCATION:https://stable.researchseminars.org/talk/PatC/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lingfu Zhang (Princeton)
DTSTART:20211029T163000Z
DTEND:20211029T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/47
DESCRIPTION:Title: The environment seen from a geodesic in last-passage percolation\
nby Lingfu Zhang (Princeton) as part of Probability and the City Seminar\n
\n\nAbstract\nIn exponential directed last-passage percolation\, each vert
ex in Z^2 is assigned an i.i.d. exponential weight\, and the geodesic betw
een a pair of vertices refers to the up-right path connecting them\, with
the maximum total weight along the path. It is a natural question to ask w
hat a geodesic looks like locally\, and how weights on and nearby the geod
esic behave. In this talk\, I will present some new results on this. We sh
ow convergence of the distribution of the ‘environment’ as seen from a
typical point along the geodesic\, and convergence of the corresponding e
mpirical measure\, as the geodesic length goes to infinity. In addition\,
we obtain an explicit description of the limiting environment\, which depe
nds on the direction of the geodesic. This in principle enables one to com
pute all the local statistics of the geodesic\, and I will talk about some
surprising and interesting examples. This is based on joint work with Jam
es Martin and Allan Sly.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firas Rassoul-Agha (Utah)
DTSTART:20211210T173000Z
DTEND:20211210T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/48
DESCRIPTION:Title: Geodesic Length in First-Passage Percolation\nby Firas Rassoul-Ag
ha (Utah) as part of Probability and the City Seminar\n\n\nAbstract\nWe st
udy first-passage percolation through related optimization problems over p
aths of restricted length. The path length variable is in duality with a s
hift of the weights. This puts into a convex duality framework old observa
tions about the convergence of the normalized Euclidean length of geodesic
s due to Hammersley and Welsh\, Smythe and Wierman\, and Kesten\, and lead
s to new results about geodesic length and the regularity of the shape fun
ction as a function of the weight shift. For points far enough away from t
he origin\, the ratio of the geodesic length and the $\\ell^1$ distance to
the endpoint is uniformly bounded away from one. The shape function is a
strictly concave function of the weight shift. Atoms of the weight distrib
ution generate singularities\, that is\, points of nondifferentiability\,
in this function. We generalize to all distributions\, directions and dime
nsions an old singularity result of Steele and Zhang for the planar Bernou
lli case. When the weight distribution has two or more atoms\, a dense set
of shifts produce singularities. The results come from a combination of t
he convex duality\, the shape theorems of the different first-passage opti
mization problems\, and modification arguments. This is joint work with Ar
jun Krishnan and Timo Seppalainen.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milind Hegde (UC Berkeley)
DTSTART:20211008T163000Z
DTEND:20211008T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/49
DESCRIPTION:Title: Brownianity in KPZ\nby Milind Hegde (UC Berkeley) as part of Prob
ability and the City Seminar\n\n\nAbstract\nThe KPZ universality class is
believed to contain a very broad collection of models of stochastic growth
. A theme in KPZ that has developed a great deal over the last 15 years\,
and particularly in recent years\, is the presence of Brownian behaviour--
-the classical kind of universality---in many natural objects. In this tal
k I will survey some of the results in the zero-temperature setting---conc
erning objects such as last passage percolation\, the Airy_2 process\, and
the KPZ fixed point---focusing on recent advances in obtaining and applyi
ng quantitative process-level Brownian comparisons of the Airy_2 process\,
as well as connections to the behaviour of geodesics in last passage perc
olation. Based on joint work with Jacob Calvert\, Ivan Corwin\, Alan Hammo
nd\, and Konstantin Matetski.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Yang (Stanford)
DTSTART:20211203T173000Z
DTEND:20211203T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/50
DESCRIPTION:Title: KPZ and Boltzmann-Gibbs\nby Kevin Yang (Stanford) as part of Prob
ability and the City Seminar\n\n\nAbstract\nThe KPZ equation is a stochast
ic PDE whose derivative conjecturally provides a universal model for "hydr
odynamic fluctuations". This is one version of the weak KPZ universality c
onjecture\, which has drawn significant attention in the past few decades.
We will discuss recent work on this conjecture for hydrodynamic limit flu
ctuations of general interacting particle systems. The key ingredient is a
Boltzmann-Gibbs principle for general systems\, whose applications beyond
KPZ and whose potential refinements will both be discussed as well.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin McSwiggen (NYU)
DTSTART:20211022T163000Z
DTEND:20211022T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/51
DESCRIPTION:Title: Random matrix models arising from projections of orbital measures
\nby Colin McSwiggen (NYU) as part of Probability and the City Seminar\n\n
\nAbstract\nA number of widely studied random matrix models can be realize
d as projections of invariant measures on group orbits. Examples include
the randomized Horn's problem\, the randomized Schur's problem\, and the o
rbital corners process. In this talk we will introduce a general framewor
k that unifies these models in the case of coadjoint orbits of a compact L
ie group. We will present both recent and classical results that hold in
this general setting\, and we will discuss applications to combinatorial r
epresentation theory and quantum information theory. The talk will be acc
essible to probabilists without a background in Lie theory or representati
on theory. Results presented will include joint work with Jean-Bernard Zu
ber\, Robert Coquereaux\, and Benoît Collins.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Kahn (Rutgers)
DTSTART:20220304T173000Z
DTEND:20220304T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/52
DESCRIPTION:Title: Linear cover time is exponentially unlikely\nby Jeff Kahn (Rutger
s) as part of Probability and the City Seminar\n\n\nAbstract\nProving a 20
09 conjecture of Itai Benjamini\, we show:\n\nFor any $C$ there is $c > 0$
so that for any simple random walk on an $n$-vertex graph $G$\, the proba
bility 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 sta
tement for Markov chains in which all transition probabilities are less th
an a suitable function of $C$.\n\nJoint with Quentin Dubroff.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emma Bailey (CUNY)
DTSTART:20220128T173000Z
DTEND:20220128T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/53
DESCRIPTION:Title: Large deviations of Selberg’s central limit theorem\, and random ma
trix theory connections\nby Emma Bailey (CUNY) as part of Probability
and the City Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PatC/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Koralov (Maryland)
DTSTART:20220204T173000Z
DTEND:20220204T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/54
DESCRIPTION:Title: Perturbations of Parabolic Equations and Diffusion Processes with Deg
eneration: Boundary Problems and Metastability\nby Leonid Koralov (Mar
yland) as part of Probability and the City Seminar\n\n\nAbstract\nWe study
diffusion processes in a bounded domain with absorbing or reflecting boun
dary. The generator of the process is assumed to contain two terms: the ma
in term that degenerates on the boundary in a direction orthogonal to the
boundary and a small non-degenerate perturbation. Understanding the behavi
or of such processes allows us to study the stabilization of solutions to
the corresponding parabolic equations with a small parameter. Metastabilit
y effects arise in this case: the asymptotics of solutions\, as the size o
f the perturbation tends to zero\, depends on the time scale. Initial-boun
dary value problems with both the Dirichet and the Neumann boundary condit
ions will be considered. The talk is based on joint work with M. Freidlin.
\n
LOCATION:https://stable.researchseminars.org/talk/PatC/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximilian Nitzscher (NYU Courant)
DTSTART:20220211T173000Z
DTEND:20220211T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/55
DESCRIPTION:Title: Phase transition for level-set percolation of the membrane model\
nby Maximilian Nitzscher (NYU Courant) as part of Probability and the City
Seminar\n\n\nAbstract\nWe consider level-set percolation for the Gaussian
membrane model on the integer lattice in dimensions five and higher\, and
establish that as h varies\, a non-trivial percolation phase transition f
or the level-set above level h occurs at some finite critical level\, whic
h we show to be positive in high dimensions. Moreover\, we demonstrate the
existence of a strongly subcritical phase\, in which we provide bounds fo
r the connectivity function of the level-set above h\, and a strongly supe
rcritical phase\, in which we characterize the geometry of the level-set a
bove level h. As a main tool\, we present novel decoupling inequalities fo
r the membrane model\, which are instrumental in the study of both the sub
critical and supercritical phases of its level-sets. This talk is based on
joint work with Alberto Chiarini.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Berestycki (Oxford)
DTSTART:20220218T173000Z
DTEND:20220218T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/56
DESCRIPTION:Title: The extremal point process of branching Brownian motion in $\\R^d$\nby Julien Berestycki (Oxford) as part of Probability and the City Semin
ar\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 fro
m the origin (at a large time $t$)? If one conditions by what happened ear
ly on in the process\, in which direction are we likely to fond the furthe
st particle? Can one describe the structure of the extremal point process
at large times? Those questions were already well understood for the case
$d=1$. IN this talk I will present some recent results concerning the mult
idimensional case.\nBased on a joint work with Yujin H. Kim\, Eyal Lubetzk
y\, Bastien Mallein\, Ofer Zeitouni.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hutchcroft (Caltech)
DTSTART:20220225T173000Z
DTEND:20220225T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/57
DESCRIPTION:Title: Critical percolation on the hierarchical lattice\nby Tom Hutchcro
ft (Caltech) as part of Probability and the City Seminar\n\n\nAbstract\nWe
consider long-range percolation on the hierarchical lattice\, a highly sy
mmetric ultrametric space that serves as a toy model for the Euclidean lat
tice Z^d. We will outline how to prove up-to-constants estimates on point-
to-point connection probabilities for the model at criticality and outline
several open problems regarding further critical exponents for the model.
\n
LOCATION:https://stable.researchseminars.org/talk/PatC/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Sidorova (University College London)
DTSTART:20220311T173000Z
DTEND:20220311T183000Z
DTSTAMP:20260404T095118Z
UID:PatC/58
DESCRIPTION:Title: Localisation and delocalisation in the parabolic Anderson model\n
by Nadia Sidorova (University College London) as part of Probability and t
he City Seminar\n\n\nAbstract\nThe parabolic Anderson problem is the Cauch
y problem for the heat equation on the integer lattice with random potenti
al. It describes the mean-field behaviour of a continuous-time branching r
andom walk. It is well-known that\, unlike the standard heat equation\, th
e solution of the parabolic Anderson model exhibits strong localisation. I
n particular\, for a wide class of iid potentials it is localised at just
one point. However\, in a partially symmetric parabolic Anderson model\, t
he one-point localisation breaks down for heavy-tailed potentials and rema
ins unchanged for light-tailed potentials\, exhibiting a range of phase tr
ansitions.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-François Rodriguez (Imperial College London)
DTSTART:20220325T163000Z
DTEND:20220325T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/59
DESCRIPTION:Title: Critical exponents for three-dimensional percolation models with long
-range dependence\nby Pierre-François Rodriguez (Imperial College Lon
don) as part of Probability and the City Seminar\n\n\nAbstract\nWe will re
port on recent progress regarding the near-critical behavior of certain st
atistical mechanics models in dimension three. Our results deal with the p
hase transition associated to two percolation problems involving the Gauss
ian free field (GFF) in 3D. In one case\, they determine a unique “fixed
point” corresponding to the transition\, which is proved to obey Fisher
’s scaling law. This is one of several relations classically conjectured
by physicists to hold on the grounds of a corresponding scaling ansatz.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Van Peski (MIT)
DTSTART:20220401T163000Z
DTEND:20220401T173000Z
DTSTAMP:20260404T095118Z
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-a
dic matrices have been studied since the late 1980s as natural models for
random groups appearing in number theory and combinatorics. Recently it ha
s also become clear that the theory has close structural parallels with si
ngular values of complex random matrices\, bringing new techniques from in
tegrable probability and motivating new questions. After outlining this ar
ea (no background in p-adic matrices will be assumed)\, I will discuss res
ults on the distribution of analogues of singular values for products of m
any random p-adic matrices. Both prelimit and limit objects exhibit much m
ore spatial independence than their analogues for complex matrices\, often
with surprising results. In different regimes we can prove Gaussian limit
s\, an intriguing new discrete Poisson-type local limit (yielding a local
interacting particle system on $\\mathbb{Z}$ similar to $q$-TASEP)\, and c
onvergence of global bulk fluctuations to a certain explicit Gaussian proc
ess.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Salez (Université Paris-Dauphine & PSL)
DTSTART:20220408T163000Z
DTEND:20220408T173000Z
DTSTAMP:20260404T095118Z
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://stable.researchseminars.org/talk/PatC/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Dunlap (NYU Courant)
DTSTART:20220415T163000Z
DTEND:20220415T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/62
DESCRIPTION:Title: Nonlinear weak-noise stochastic heat equations in two dimensions\
nby Alex Dunlap (NYU Courant) as part of Probability and the City Seminar\
n\n\nAbstract\nI will discuss a two-dimensional stochastic heat equation i
n the weak noise regime with a nonlinear noise strength. I will explain ho
w pointwise statistics of solutions to this equation\, as the correlation
length of the noise is taken to 0 but the noise is attenuated by a logarit
hmic factor\, can be related to a forward-backward stochastic differential
equation (FBSDE) depending on the nonlinearity. I will also discuss two c
ases in which the FBSDE can be explicitly solved: the linear stochastic he
at equation\, for which we recover the log-normal behavior proved by Carav
enna\, Sun\, and Zygouras\, and branching Brownian motion/super-Brownian m
otion\, 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://stable.researchseminars.org/talk/PatC/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hubert Lacoin (IMPA)
DTSTART:20220422T163000Z
DTEND:20220422T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/63
DESCRIPTION:by Hubert Lacoin (IMPA) as part of Probability and the City Se
minar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PatC/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Tassion (ETH Zurich)
DTSTART:20220429T163000Z
DTEND:20220429T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/64
DESCRIPTION:by Vincent Tassion (ETH Zurich) as part of Probability and the
City Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PatC/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Das (Columbia)
DTSTART:20220506T163000Z
DTEND:20220506T173000Z
DTSTAMP:20260404T095118Z
UID:PatC/65
DESCRIPTION:Title: Path properties of the KPZ Equation and related polymers\nby Saya
n Das (Columbia) as part of Probability and the City Seminar\n\n\nAbstract
\nThe KPZ equation is a fundamental stochastic PDE that can be viewed as t
he log-partition function of continuum directed random polymer (CDRP). In
this talk\, we will first focus on the fractal properties of the tall peak
s of the KPZ equation. This is based on separate joint works with Li-Cheng
Tsai and Promit Ghosal. In the second part of the talk\, we will study th
e KPZ equation through the lens of polymers. In particular\, we will discu
ss localization aspects of CDRP that will shed light on certain properties
of the KPZ equation such as ergodicity and limiting Bessel behaviors arou
nd the maximum. This is based on joint work with Weitao Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/PatC/65/
END:VEVENT
END:VCALENDAR