BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Todd Kemp (UCSD)
DTSTART:20200508T190000Z
DTEND:20200508T200000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/1
DESCRIPTION:Title: Geometric matrix Brownian motion and the Lima Bean Law\n
by Todd Kemp (UCSD) as part of Integrable Probability\n\n\nAbstract\nGeome
tric matrix Brownian motion is the solution (in $N\\times N$ matrices) to
the stochastic differential equation $dG_t = G_t dZ_t$\, $G_0 = I$\, where
$Z_t$ is a Ginibre Brownian motion (all independent complex Brownian moti
on entries). It can also be described as the standard Brownian motion on t
he Lie group $\\mathrm{GL}(N\,\\mathbb{C})$. For $N>2$\, with probability
$1$ it is not a normal matrix for any $t>0$. Over the last 5 years\, we ha
ve made progress in understanding its asymptotic moments and fluctuations\
, but the non-normality (and lack of explicit symmetry) has made understan
ding its large-$N$ limit empirical eigenvalue distribution quite challengi
ng.\n\nThe tools around the circular law are now rich and provide a (log)
potential course of action to understand the eigenvalues. There are two si
des to this problem in general\, both quite difficult: proving that the em
pirical law of eigenvalues converges (which amounts to strong tightness co
nditions on singular values)\, and computing what it converges {\\em to}.
In the case of the geometric matrix Brownian motion\, the question of conv
ergence is still a work in progress\; but in recent joint work with Bruce
Driver and Brian Hall\, we have explicitly calculated the limit empirical
eigenvalue distribution. It has an analytic density with a nice polar deco
mposition\, supported on a region that resembles a lima bean for small $t>
0$\, then folds over and becomes a topological annulus when $t>4$.\n\nOur
methods blend stochastic analysis\, complex analysis\, and PDE\, and appro
ach the log potential in a new way that we hope will be useful in a wider
context.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yun Li (University of Wisconsin\, Madison)
DTSTART:20200522T150000Z
DTEND:20200522T160000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/2
DESCRIPTION:Title: Pre-seminar for Benedek Valko's talk on the stochastic zeta
function\nby Yun Li (University of Wisconsin\, Madison) as part of Int
egrable Probability\n\n\nAbstract\nThis pre-seminar will provide relevant
background to Benedek Valko's seminar later in the day.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benedek Valko (University of Wisconsin\, Madison)
DTSTART:20200522T180000Z
DTEND:20200522T190000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/3
DESCRIPTION:Title: The stochastic zeta function\nby Benedek Valko (Universi
ty of Wisconsin\, Madison) as part of Integrable Probability\n\n\nAbstract
\nThe finite circular beta-ensembles and their point process scaling limit
can be represented as the spectra of certain random differential operator
s. These operators can be realized on a single probability space so that t
he point process scaling limit is a consequence of an operator level limit
. The construction allows the derivation of the scaling limit of the norma
lized characteristic polynomials of the finite models to a random analytic
function\, which we call the stochastic zeta function. I will review thes
e representations and constructions\, and present a couple of applications
. Joint with B. Virág (Toronto).\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bufetov (Bonn)
DTSTART:20200605T160000Z
DTEND:20200605T170000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/4
DESCRIPTION:Title: Interacting particle systems and random walks on Hecke algeb
ras\nby Alexey Bufetov (Bonn) as part of Integrable Probability\n\n\nA
bstract\nMulti-species versions of several interacting particle systems\,
including ASEP\, q-TAZRP\, and k-exclusion processes\, can be interpreted
as random walks on Hecke algebras. In the talk I will discuss this connect
ion and its probabilistic applications.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Kuan (Texas A&M)
DTSTART:20200605T171500Z
DTEND:20200605T181500Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/5
DESCRIPTION:Title: Algebraic symmetries of multi--species models\nby Jeff K
uan (Texas A&M) as part of Integrable Probability\n\n\nAbstract\nWe review
some recent results on multi--species interacting particle systems and ve
rtex models. In particular\, we show how the quantum group and Coxeter gro
up symmetries lead to duality\, color-position symmetry\, contour integral
formulas\, and hydrodynamics.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaetan Borot (Bonn)
DTSTART:20200619T150000Z
DTEND:20200619T160000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/6
DESCRIPTION:Title: Introduction to geometric recursion\nby Gaetan Borot (Bo
nn) as part of Integrable Probability\n\n\nAbstract\nThe geometric recursi
on is a general framework to make natural constructions attached to surfac
es S of any topology\, by using the idea of cutting the surface into eleme
ntary pieces -- I will explain what "natural" means. Examples of natural c
onstructions are certain measures on the space Teich(S) of conformal class
es of metrics on surfaces\, which can be used to talk about ensembles of r
andom surfaces\, and statistical properties of simple geodesics on them\,
and can be approached by recursion on the topology generalizing Mirzakhani
's recursion. I will hint at other "natural constructions" that may fit in
this framework\, such as spectral statistics and measures from quantum gr
avity.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomohiro Sasamoto (Tokyo Institute of Technology)
DTSTART:20200703T130000Z
DTEND:20200703T140000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/7
DESCRIPTION:Title: Spin current statistics for the quantum 1D XX spin chain and
the Bessel kernel\nby Tomohiro Sasamoto (Tokyo Institute of Technolog
y) as part of Integrable Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (University of Toronto)
DTSTART:20200703T170000Z
DTEND:20200703T190000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/8
DESCRIPTION:Title: From TASEP to the KPZ fixed point and KP\nby Jeremy Quas
tel (University of Toronto) as part of Integrable Probability\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Knizel (Columbia University)
DTSTART:20200710T140000Z
DTEND:20200710T150000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/9
DESCRIPTION:Title: Invariant measure for the open KPZ equation\nby Alisa Kn
izel (Columbia University) as part of Integrable Probability\n\n\nAbstract
\nI will talk about a construction of an invariant measure for the open KP
Z equation on a bounded interval with Neumann boundary conditions. The app
roach relies on two main ingredients. The first is that open ASEP converge
s to open KPZ under weakly asymmetric scaling around the triple point of t
he phase diagram. The second is that the invariant measure of open ASEP ca
n be computed exactly via Askey-Wilson processes\, a variant of the matrix
product ansatz. This construction is a joint work with Ivan Corwin.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeni Dimitrov (Columbia University)
DTSTART:20200710T150000Z
DTEND:20200710T160000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/10
DESCRIPTION:Title: Two-point convergence of the stochastic six-vertex model to
the Airy process\nby Evgeni Dimitrov (Columbia University) as part of
Integrable Probability\n\n\nAbstract\nWe consider the stochastic six-vert
ex model in the quadrant started with step initial data. We will show that
\, under suitable scaling\, the two-point distribution of the height funct
ion converges to the two-point distribution of the Airy process.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Hammond (UC Berkeley)
DTSTART:20200717T170000Z
DTEND:20200717T180000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/11
DESCRIPTION:by Alan Hammond (UC Berkeley) as part of Integrable Probabilit
y\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Fyodorov (King's College London)
DTSTART:20200724T140000Z
DTEND:20200724T150000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/12
DESCRIPTION:Title: On eigenvector statistics in non-normal random matrices
\nby Yan Fyodorov (King's College London) as part of Integrable Probabilit
y\n\n\nAbstract\nI will discuss some results\, both old and more recent\,
on 'non-orthogonality overlap matrix' between left and right eigenvectors
of non-normal random matrices. Motivations range from understanding eigenv
alue dynamics under matrix perturbations to relevance for random matrix mo
dels describing chaotic wave scattering.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinho Baik (University of Michigan)
DTSTART:20200724T170000Z
DTEND:20200724T180000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/13
DESCRIPTION:Title: Relaxation time limit of periodic TASEP\nby Jinho Baik
(University of Michigan) as part of Integrable Probability\n\n\nAbstract\n
The marginals of a spatially periodic TASEP converge to non-trivial limits
when both the period and the time tend to infinity in a critical way. To
compare the periodic case and the infinite line KPZ fixed point\, we will
focus primarily on the one-point distribution for the step initial conditi
on and show how the formula changes from the GUE Tracy-Widom distribution
of the infinite line KPZ fixed point. We will discuss both the Fredholm de
terminant formula and the differential equation formula. The later formula
will tell us connections to integrable differential equations.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Gorin (MIT and University of Wisconsin\, Madison)
DTSTART:20200807T170000Z
DTEND:20200807T190000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/14
DESCRIPTION:by Vadim Gorin (MIT and University of Wisconsin\, Madison) as
part of Integrable Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20200814T170000Z
DTEND:20200814T180000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/15
DESCRIPTION:by Leonid Petrov (University of Virginia) as part of Integrabl
e Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li-Cheng Tsai (Rutgers University)
DTSTART:20200821T170000Z
DTEND:20200821T180000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/16
DESCRIPTION:Title: Moments and tails of stochastic PDEs\nby Li-Cheng Tsai
(Rutgers University) as part of Integrable Probability\n\n\nAbstract\nThis
talk focuses on two aspects of stochastic PDEs: moments and large deviati
ons. For the Stochastic Heat Equation (with multiplicative noise) and the
Kardar--Parisi--Zhang equation\, I will explain how these two aspects are
interconnected\, and how to obtain precise descriptions of these two aspec
ts.\n\nThe talk will cover joint work with Sayan Das and joint work with Y
u Gu and Jeremy Quastel.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amol Aggarwal (CMI and Columbia University)
DTSTART:20200821T180000Z
DTEND:20200821T190000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/17
DESCRIPTION:Title: Limit Shapes and Local Statistics for the Stochastic Six-Ve
rtex Model\nby Amol Aggarwal (CMI and Columbia University) as part of
Integrable Probability\n\n\nAbstract\nIn this talk we outline how limit sh
apes for the stochastic six-vertex model under arbitrary initial data can
be proven using hydrodynamical limit methods from the context of interacti
ng particle systems. This proceeds by first establishing the limit shape r
esult for specific (double-sided Bernoulli) initial data\, which is often
exactly solvable\, and then by extending it to general initial profiles. I
f time permits\, we will also discuss convergence of local statistics to t
he translation-invariant\, extremal Gibbs measure of the appropriate slope
.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Warren (University of Warwick)
DTSTART:20200828T140000Z
DTEND:20200828T150000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/18
DESCRIPTION:Title: Reflecting Brownian motions and point-to-line last passage
percolation\nby Jon Warren (University of Warwick) as part of Integra
ble Probability\n\n\nAbstract\nThe all-time supremum of a Brownian motion
with negative drift is exponentially distributed. A generalization of this
classical fact to random matrices is the statement that the supremum of
the largest eigenvalue of a Hermitian Brownian motion with drift is equal
in distribution to a point-to-line last passage time through a field of e
xponentially distributed random variables. The same distribution arises a
s a marginal of the stationary distribution of a system of reflecting Brow
nian motions with a wall. I will discuss these results and their finite
temperature analogues which link exponential functionals of Brownian moti
on to the log gamma polymer.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Zygouras (University of Warwick)
DTSTART:20200828T150000Z
DTEND:20200828T160000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/19
DESCRIPTION:Title: Variants of geometric RSK and polymers\nby Nikos Zygour
as (University of Warwick) as part of Integrable Probability\n\n\nAbstract
\nWe will review the use of geometric Robinson-Schensted-Knuth corresponde
nce and how this can be applied to obtain laws of polymer models. We will
focus\, in particular\, on more recent work with E. Bisi and N. O'Connell
where we constructed the geometric Burge correspondence and applied it to
obtain the law of replicas of partition functions.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20201009T183000Z
DTEND:20201009T200000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/20
DESCRIPTION:Title: Random polymers and symmetric functions\nby Leonid Petr
ov (University of Virginia) as part of Integrable Probability\n\n\nAbstrac
t\nI will survey integrable random polymers (based on gamma / inverse gamm
a or beta distributed weights)\, and explain their connection to symmetric
functions (respectively\, gl_n Whittaker and new spin Whittaker functions
). The work on spin Whittaker functions is joint with Matteo Mucciconi.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Duits (KTH)
DTSTART:20201023T183000Z
DTEND:20201023T200000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/21
DESCRIPTION:Title: CLTs for biorthogonal ensembles: Beyond the Strong Szegö L
imit Theorem\nby Maurice Duits (KTH) as part of Integrable Probability
\n\n\nAbstract\nThe Strong Szegö Limit Theorem for Toeplitz determinants
implies a CLT for linear statistics for eigenvalues of a CUE matrix. The f
irst part of the talk will be an overview of results on various extensions
of the Strong Szegö Limit theorem to determinants of truncated exponenti
als of banded matrices\, providing CLTs for more general classes of determ
inantal point processes including orthogonal polynomial ensembles on the r
eal line and unit circle. A time-dependent analogue can be used tot establ
ish Gaussian Free Field fluctuations in certain non-colliding process and
random tilings of planar domains. The second part of the talk will focus o
n discussing a recent joint work with Fahs and Kozhan on Multiple Orthogon
al Polynomials Ensembles. Such models include Gaussian Unitary Ensembles w
ith external source\, complex Wishart matrices\, two matrix models and cer
tain specialization of the Schur process. A new feature in those models is
that there is no canonical choice for the recurrence matrix.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurt Johansson (KTH)
DTSTART:20201112T193000Z
DTEND:20201112T210000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/22
DESCRIPTION:Title: Multivariate normal approximation for traces of random unit
ary matrices\nby Kurt Johansson (KTH) as part of Integrable Probabilit
y\n\n\nAbstract\nConsider an n x n random unitary matrix U taken with resp
ect to normalized Haar measure. It is a well known consequence of the stro
ng Szego limit theorem that the traces of powers of U converge to independ
ent complex normal random variables as n grows. I will discuss a recent re
sult where we obtain a super-exponential rate of convergence in total vari
ation distance between the traces of the first m powers of an n × n rando
m unitary matrices and a 2m-dimensional Gaussian random vector. This gener
alizes previous results in the scalar case\, which answered a conjecture b
y Diaconis\, to the multivariate setting. We are especially interested in
the regime where m grows with n. The problem on how the rate of convergenc
e changes as m grows with n was raised recently by Sarnak. The result we o
btain gives the dependence on the dimensions m and n in the estimate with
explicit constants for m almost up to the square root of n. This is joint
work with Gaultier Lambert.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaoyang Huang (NYU)
DTSTART:20201211T193000Z
DTEND:20201211T210000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/23
DESCRIPTION:Title: Height Fluctuations of Random Lozenge Tilings Through Nonin
tersecting Random Walks\nby Jiaoyang Huang (NYU) as part of Integrable
Probability\n\n\nAbstract\nIn this talk\, we will discuss global fluctuat
ions of random lozenge tilings of polygonal domains. We study their height
functions from a dynamical pointview\, by identifying lozenge tilings wit
h nonintersecting Bernoulli random walks. For a large class of polygons wh
ich have exactly one horizontal upper boundary edge\, we show that these r
andom height functions converge to a Gaussian Free Field as predicted by K
enyon and Okounkov.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Sodin (QMUL)
DTSTART:20201130T200000Z
DTEND:20201130T213000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/24
DESCRIPTION:Title: A random operator constructed from the representations of t
he symmetric group\nby Sasha Sodin (QMUL) as part of Integrable Probab
ility\n\n\nAbstract\nWe shall discuss the construction of an amusing rando
m operator acting on certain representations of the infinite symmetric gro
up and sharing some features with the Anderson model. Particularly\, we sh
ow that the spectrum of the operator exhibits so-called quantum Lifshitz t
ails\, characteristic of d-dimensional random operators. The operator is a
lso closely related to a randomised version of the fifteen puzzle on an in
finite board\; this connection plays a central role in the proof of the ma
in result. Based on joint work with Ohad N. Feldheim.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shirshendu Ganguly (Berkeley)
DTSTART:20201123T193000Z
DTEND:20201123T210000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/25
DESCRIPTION:Title: Stability and chaos in dynamical last passage percolation\nby Shirshendu Ganguly (Berkeley) as part of Integrable Probability\n\n
\nAbstract\nMany complex disordered systems in statistical mechanics are c
haracterized by intricate energy landscapes. The ground state\, the config
uration with lowest energy\, lies at the base of the deepest valley. In im
portant examples\, such as Gaussian polymers and spin glass models\, the l
andscape has many valleys and 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 disorder of the model is slightly pertu
rbed.\n\nIn this talk\, we will discuss a recent work computing the critic
al exponent that governs the onset of chaos in a dynamic manifestation of
a canonical model in the Kardar-Parisi-Zhang [KPZ] universality class\, Br
ownian last passage percolation [LPP]. In this model in its static form\,
semi-discrete polymers advance through Brownian noise\, their energy given
by the integral of the white noise encountered along their journey. A gro
und state is a geodesic\, of extremal energy given its endpoints.\n\nWe wi
ll show that when Brownian LPP is perturbed by evolving the disorder under
an Ornstein-Uhlenbeck flow\, for polymers of length n\, a sharp phase tra
nsition marking the onset of chaos is witnessed at the critical time $n^{-
1/3}$\, by showing that the overlap between the geodesics at times zero an
d $t > 0$ that travel a given distance of order is of order $n$ when $t \\
ll n^{-1/3}$\; and of a smaller order when $t \\gg n^{-1/3}$. We expect th
is exponent to be universal across a wide range of interface models. The p
roof relies on Chatterjee's harmonic analytic theory of equivalence of sup
erconcentration and chaos in Gaussian spaces and a refined understanding o
f the static landscape geometry of Brownian LPP.\n\nThe talk is based on j
oint work with Alan Hammond (https://arxiv.org/abs/2010.05837 and the comp
anion paper https://arxiv.org/abs/2010.05836).\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sayan Das (Columbia)
DTSTART:20210226T190000Z
DTEND:20210226T200000Z
DTSTAMP:20260422T212609Z
UID:IntegrableProbability/26
DESCRIPTION:Title: Fractal Properties of the KPZ temporal Process\nby Saya
n Das (Columbia) as part of Integrable Probability\n\n\nAbstract\nIn this
talk\, we study the macroscopic fractal properties of the Cole-Hopf soluti
on of the Kardar-Parisi-Zhang (KPZ) equation. We show that under the expon
ential transformation of the time variable\, the peaks of the KPZ height f
unction mutate from being monofractal to multifractal. Our proof relies on
three main ingredients: i) multipoint composition law of the KPZ equation
ii) Gibbsian line ensemble techniques iii) short time tail probabilities
of KPZ height function. Joint work with Promit Ghosal.\n
LOCATION:https://researchseminars.org/talk/IntegrableProbability/26/
END:VEVENT
END:VCALENDAR