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BEGIN:VEVENT
SUMMARY:Kevin Yang (Stanford)
DTSTART:20201002T183000Z
DTEND:20201002T193000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/1
DESCRIPTION:Title: Kardar-Parisi-Zhang equation from some long-range particle sy
stems\nby Kevin Yang (Stanford) as part of Columbia SPDE Seminar\n\n\n
Abstract\nWe discuss some new results on the Kardar-Parisi-Zhang equation
as the continuum limit for height functions associated to long-range varia
tions on ASEP and open ASEP. The method of proof is primarily based on loc
alizing certain aspects of the dynamical approach in the energy solution t
heory of Goncalves-Jara. We conclude with future applications of this meth
od to study SPDE continuum limits for other non-integrable interacting par
ticle systems.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hubert Lacoin (IMPA)
DTSTART:20201016T183000Z
DTEND:20201016T193000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/2
DESCRIPTION:Title: The continuum directed polymer in Lévy Noise as a scaling li
mit\nby Hubert Lacoin (IMPA) as part of Columbia SPDE Seminar\n\n\nAbs
tract\nDirected polymer in a random environment is one of the simplest and
most studied disordered models in statistical mechanics. The directed pol
ymer measure is a distribution on the set of nearest neighbor paths of len
gth $N$ in $\\mathbb{Z}^d$ which to each paths gives a probability proport
ional to $\\prod_{n=1}^N (1+\\beta \\eta_{n\,S_n})$ where $\\beta>0$ is a
fixed parameter and $(\\eta_{n\,x})$ $n\\in \\mathbb N$\, $x\\in \\mathbb{
Z}^d$ is (a fixed realization of) a field of IID random variables. The aim
of the talk is to introduce a continuum version of the directed polymer m
odel which appears as a scaling limit when considering an "intermediate di
sorder regime" (sending $N$ to infinity and $\\beta$ to zero at an appropr
iate rate) for a directed polymer model with heavy-tailed random environme
nt. The model is the Levy Noise analog of the "Continuum Directed Random P
olymer" introduced by Alberts\, Khanin and Quastel and present strong conn
ections with the Stochastic Heat Equation with multiplicative Lévy noise.
\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Cosco (Weizmann Institute)
DTSTART:20201016T193500Z
DTEND:20201016T200000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/3
DESCRIPTION:Title: The stochastic heat equation (SHE) and the Kardar-Parisi-Zhan
g (KPZ) equation in dimension d ≥ 3\nby Clément Cosco (Weizmann Ins
titute) as part of Columbia SPDE Seminar\n\n\nAbstract\nThere has been rec
ent progress on the study of the mollified SHE and KPZ equation in higher
dimension as the mollification parameter is switched off. We present a sel
ection of these results\, as well as the related results on the 1+d-dimens
ional directed polymer model which is directly linked to the equations.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yier Lin (Columbia)
DTSTART:20201030T183000Z
DTEND:20201030T193000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/4
DESCRIPTION:Title: Short time large deviations of the KPZ equation\nby Yier
Lin (Columbia) as part of Columbia SPDE Seminar\n\n\nAbstract\nWe establis
h the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochasti
c Heat Equation with multiplicative noise in one spatial dimension. That i
s\, we introduce a small parameter $\\sqrt{\\epsilon}$ to the noise\, and
establish an LDP for the trajectory of the solution. Such a Freidlin--Went
zell LDP gives the short-time\, one-point LDP for the KPZ equation in term
s of a variational problem. Analyzing this variational problem under the n
arrow wedge initial data\, we prove a quadratic law for the near-center ta
il and a 5/2 law for the deep lower tail. These power laws confirm existin
g physics predictions Kolokolov and Korshunov (2007)\, Kolokolov and Korsh
unov (2009)\, Meerson\, Katzav\, and Vilenkin (2016)\, Le Doussal\, Majumd
ar\, Rosso\, and Schehr (2016)\, and Kamenev\, Meerson\, and Sasorov (2016
). Joint work with Li-Cheng Tsai.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykhaylo Shkolnikov (Princeton)
DTSTART:20201106T193000Z
DTEND:20201106T203000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/5
DESCRIPTION:Title: A sharp interface limit in the Giacomin-Lebowitz model of pha
se segregation\nby Mykhaylo Shkolnikov (Princeton) as part of Columbia
SPDE Seminar\n\n\nAbstract\nWe will discuss the segregation process of tw
o immiscible substances (e.g.\, oil and water) that have been mixed togeth
er. In 1996\, Giacomin and Lebowitz proposed a mathematical model for this
process that can be viewed as an alternative to the celebrated Cahn-Hilli
ard equation. They also conjectured that\, in their model\, the first stag
e of the phase segregation process\, in which the mixture separates into t
wo distinct regions\, can be captured on the large scale by a suitable fre
e boundary problem. Mykhaylo will describe the latter free boundary proble
m and some aspects of its analysis. Jiacheng will then explain how it aris
es in the context of the Giacomin-Lebowitz model.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Zhang (Princeton)
DTSTART:20201106T203500Z
DTEND:20201106T210000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/6
DESCRIPTION:Title: A sharp interface limit in the Giacomin-Lebowitz model of pha
se segregation\nby Jiacheng Zhang (Princeton) as part of Columbia SPDE
Seminar\n\n\nAbstract\nWe will discuss the segregation process of two imm
iscible substances (e.g.\, oil and water) that have been mixed together. I
n 1996\, Giacomin and Lebowitz proposed a mathematical model for this proc
ess that can be viewed as an alternative to the celebrated Cahn-Hilliard e
quation. They also conjectured that\, in their model\, the first stage of
the phase segregation process\, in which the mixture separates into two di
stinct regions\, can be captured on the large scale by a suitable free bou
ndary problem. Mykhaylo will describe the latter free boundary problem and
some aspects of its analysis. Jiacheng will then explain how it arises in
the context of the Giacomin-Lebowitz model.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Friz (TU and WIAS Berlin)
DTSTART:20201204T193000Z
DTEND:20201204T203000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/7
DESCRIPTION:Title: Laplace method on rough path and model space\nby Peter Fr
iz (TU and WIAS Berlin) as part of Columbia SPDE Seminar\n\n\nAbstract\nLa
place's method allows one to obtain precise asymptotics in the large devia
tion principle. I will review the case of rough paths\, then talk about ex
tensions to rough volatility and singular SPDEs. Joint work with Paul Gass
iat (Paris)\, Paolo Pigato (Rom) and Tom Klose (Berlin).\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davar Khoshnevisan (Utah)
DTSTART:20200925T183000Z
DTEND:20200925T193000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/8
DESCRIPTION:Title: Ergodicity and CLT for SPDEs\nby Davar Khoshnevisan (Utah
) as part of Columbia SPDE Seminar\n\n\nAbstract\nI will summarize some of
the recent collaborative work with Le Chen\, David Nualart\, and Fei Pu i
n which we characterize when the solution to a large family of parabolic s
tochastic PDE is ergodic in its spatial variable. We also identify when th
ere are Gaussian fluctuations associated to the resulting ergodic theorem.
\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Pu (Luxembourg)
DTSTART:20200925T193500Z
DTEND:20200925T200000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/9
DESCRIPTION:Title: Ergodicity and central limit theorems for parabolic Anderson
model with delta initial condition\nby Fei Pu (Luxembourg) as part of
Columbia SPDE Seminar\n\n\nAbstract\nLet $\\{u(t\\\,\, x)\\}_{t >0\, x \\i
n\\mathbb{R}}$ denote the solution to the parabolic Anderson model with i
nitial condition $\\delta_0$ and driven by space-time white noise on $\\ma
thbb{R}_+\\times\\mathbb{R}$\, and let $\\bm{p}_t(x):=(2\\pi t)^{-1/2}\\ex
p\\{-x^2/(2t)\\}$ denote the standard Gaussian heat kernel on the line. We
prove that the random field $x\\mapsto u(t\\\,\,x)/\\bm{p}_t(x)$ is ergo
dic for every $t >0$. And we establish an associatedquantitative central l
imit theorem using Malliavin-Stein method. \nThis is based on joint work w
ith Le Chen\, Davar Khoshenvisan and David Nualart.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanghui Liu (Baruch College)
DTSTART:20210219T190000Z
DTEND:20210219T200000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/10
DESCRIPTION:Title: Numerical approximations for rough differential equations\nby Yanghui Liu (Baruch College) as part of Columbia SPDE Seminar\n\n\nA
bstract\nThe rough paths theory provides a general framework for stochasti
c differential equations driven by processes with very low regularities\,
which has important applications in finance\, statistical mechanics\, hydr
o-dynamics and so on. The numerical approximation is a crucial step while
applying these stochastic models in practice. In this talk I will introduc
e the recent results on numerical approximation for stochastic differentia
l equations\, and then focus on the Malliavin differentiability of the Eul
er schemes. The Malliavin differentiability is a key to weak convergence a
nd density convergence problems.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reiß (HU Berlin)
DTSTART:20210312T190000Z
DTEND:20210312T200000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/11
DESCRIPTION:Title: Nonparametric estimation for SPDEs via localisation\nby
Markus Reiß (HU Berlin) as part of Columbia SPDE Seminar\n\n\nAbstract\nW
e shall first discuss differences for parametric drift estimation between
stochastic ordinary and partial differential equations (SODEs/SPDEs). For
parabolic SPDEs a classical estimation approach is based on the spectral d
ecomposition of the generator\, which is assumed to be known (at least for
the main symbol). For nonparametric problems this is no longer feasible.
We consider the specific problem of estimating the space-dependent diffusi
vity of a stochastic heat equation from time-continuous observations with
local space resolution $h$. The rather counterintuitive result and its eff
iciency as $h\\to 0$ will be discussed in detail. The methodology will be
extended to cover more general semilinear SPDEs and an application to expe
rimental data from cell repolarisation will be presented.\n\nReferences:\n
Altmeyer\, R. and Reiß\, M. (2021)\, Nonparametric estimation for linear
SPDEs from local measurements\, Ann. Appl. Prob.\, to appear\, arXiv:1903.
06984\n\nAltmeyer\, R.\, Bretschneider\, T.\, Janak\, J.\, Reiß\, M. (202
0) Parameter estimation in an SPDE-model for cell repolarisation\, arXiv:2
010.06340\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Cerrai (University of Maryland)
DTSTART:20210416T180000Z
DTEND:20210416T190000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/12
DESCRIPTION:Title: On the Smoluchowski-Kramers approximation of infinite-dimens
ional systems with state-dependent friction\nby Sandra Cerrai (Univers
ity of Maryland) as part of Columbia SPDE Seminar\n\n\nAbstract\nI will gi
ve an overview of a series of results on the asymptotic behavior\, with re
spect to the small mass\, of infinite-dimensional stochastic systems descr
ibed by damped waves equation perturbed by a Gaussian noise. In particular
\, I will focus my attention on the case where the friction coefficient is
state-dependent.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurélien Deya (IECL\, Université de Lorraine)
DTSTART:20210423T180000Z
DTEND:20210423T190000Z
DTSTAMP:20260404T111321Z
UID:Columbia_SPDE/13
DESCRIPTION:Title: Nonlinear PDE models with stochastic fractional perturbation
\nby Aurélien Deya (IECL\, Université de Lorraine) as part of Columb
ia SPDE Seminar\n\n\nAbstract\nWe consider the following quadratic SPDE mo
del:\n\n$$\\mathcal{L} u= u^2+\\dot{B}\, \\quad t\\in [0\,T]\, \\\, x\\in
\\mathbb{R}^d\,$$\nwhere $\\dot{B}$ is a stochastic noise\, and $\\mathca
l{L}$ can be either: $(i)$ the heat operator $\\mathcal{L}^{\\textbf{(h)}}
u=\\partial_t u-\\Delta u$\; $(ii)$ the wave operator $\\mathcal{L}^{\\te
xtbf{(w)}} u=\\partial^2_t u-\\Delta u$\; $(iii)$ the Schrödinger operato
r $\\mathcal{L}^{\\textbf{(s)}} u=\\imath\\partial_t u-\\Delta u$.\n\nThe
dynamics can thus be seen\, on the one hand\, as the most basic stochastic
perturbation of the standard nonlinear PDE $\\mathcal{L} u= u^2$\, and on
the other hand as the most elementary nonlinear extension of the standard
SPDE $\\mathcal{L} u= \\dot{B}$.\n\nOur objective is to study the influen
ce of the roughness of $\\dot{B}$ on the equation\, and to this end\, we r
ely on the great flexibility offered by the fractional noise model\n$$\\do
t{B}:=\\frac{\\partial^{d+1}B}{\\partial t\\partial x_1\\cdots \\partial x
_d}\\\, \,$$\nwhere $B$ is a space-time fractional Brownian field of index
es $H_0\,\\ldots\,H_d\\in (0\,1)^{d+1}$.\n\nBy letting the parameters $H_i
$ vary\, we can study the transition between the regular "noiseless" situa
tion ($H_i\\approx 1$) and rougher common noise models: space-time white n
oise ($H_i=\\frac12$)\, white-in-time noise ($H_0=\\frac12$)\, spatial noi
se ($H_0\\approx 1$)\,... This gives us the opportunity to observe success
ive changes of regimes in the handling of the equation: direct treatment\,
expansion of higher orders\, renormalization procedures\,...\n\nWe will a
lso discuss about a first step toward the discretization of the equation a
bove: namely\, the discretization of the underlying "linear" model $\\math
cal{L} u=\\dot{B}$.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia_SPDE/13/
END:VEVENT
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