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BEGIN:VEVENT
SUMMARY:Kevin Yang (Stanford)
DTSTART:20201002T183000Z
DTEND:20201002T193000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/1
DESCRIPTION:Title: Kardar-Parisi-Zhang equation from some long-range particle systems\nby Kevin Yang (Stanford) as part of Columbia SPDE Seminar\n\n\nAbstrac
t\nWe discuss some new results on the Kardar-Parisi-Zhang equation as the
continuum limit for height functions associated to long-range variations o
n ASEP and open ASEP. The method of proof is primarily based on localizing
certain aspects of the dynamical approach in the energy solution theory o
f Goncalves-Jara. We conclude with future applications of this method to s
tudy SPDE continuum limits for other non-integrable interacting particle s
ystems.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hubert Lacoin (IMPA)
DTSTART:20201016T183000Z
DTEND:20201016T193000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/2
DESCRIPTION:Title: The continuum directed polymer in Lévy Noise as a scaling limit
\nby Hubert Lacoin (IMPA) as part of Columbia SPDE Seminar\n\n\nAbstract\n
Directed polymer in a random environment is one of the simplest and most s
tudied disordered models in statistical mechanics. The directed polymer me
asure is a distribution on the set of nearest neighbor paths of length $N$
in $\\mathbb{Z}^d$ which to each paths gives a probability proportional t
o $\\prod_{n=1}^N (1+\\beta \\eta_{n\,S_n})$ where $\\beta>0$ is a fixed p
arameter and $(\\eta_{n\,x})$ $n\\in \\mathbb N$\, $x\\in \\mathbb{Z}^d$ i
s (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 model wh
ich appears as a scaling limit when considering an "intermediate disorder
regime" (sending $N$ to infinity and $\\beta$ to zero at an appropriate ra
te) for a directed polymer model with heavy-tailed random environment. The
model is the Levy Noise analog of the "Continuum Directed Random Polymer"
introduced by Alberts\, Khanin and Quastel and present strong connections
with the Stochastic Heat Equation with multiplicative Lévy noise.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Cosco (Weizmann Institute)
DTSTART:20201016T193500Z
DTEND:20201016T200000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/3
DESCRIPTION:Title: The stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ)
equation in dimension d ≥ 3\nby Clément Cosco (Weizmann Institute)
as part of Columbia SPDE Seminar\n\n\nAbstract\nThere has been recent pro
gress on the study of the mollified SHE and KPZ equation in higher dimensi
on as the mollification parameter is switched off. We present a selection
of these results\, as well as the related results on the 1+d-dimensional d
irected polymer model which is directly linked to the equations.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yier Lin (Columbia)
DTSTART:20201030T183000Z
DTEND:20201030T193000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/4
DESCRIPTION:Title: Short time large deviations of the KPZ equation\nby Yier Lin (Co
lumbia) as part of Columbia SPDE Seminar\n\n\nAbstract\nWe establish the F
reidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat
Equation with multiplicative noise in one spatial dimension. That is\, we
introduce a small parameter $\\sqrt{\\epsilon}$ to the noise\, and establi
sh an LDP for the trajectory of the solution. Such a Freidlin--Wentzell LD
P gives the short-time\, one-point LDP for the KPZ equation in terms of a
variational problem. Analyzing this variational problem under the narrow w
edge initial data\, we prove a quadratic law for the near-center tail and
a 5/2 law for the deep lower tail. These power laws confirm existing physi
cs predictions Kolokolov and Korshunov (2007)\, Kolokolov and Korshunov (2
009)\, Meerson\, Katzav\, and Vilenkin (2016)\, Le Doussal\, Majumdar\, Ro
sso\, and Schehr (2016)\, and Kamenev\, Meerson\, and Sasorov (2016). Join
t work with Li-Cheng Tsai.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykhaylo Shkolnikov (Princeton)
DTSTART:20201106T193000Z
DTEND:20201106T203000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/5
DESCRIPTION:Title: A sharp interface limit in the Giacomin-Lebowitz model of phase segr
egation\nby Mykhaylo Shkolnikov (Princeton) as part of Columbia SPDE S
eminar\n\n\nAbstract\nWe will discuss the segregation process of two immis
cible substances (e.g.\, oil and water) that have been mixed together. In
1996\, Giacomin and Lebowitz proposed a mathematical model for this proces
s that can be viewed as an alternative to the celebrated Cahn-Hilliard equ
ation. They also conjectured that\, in their model\, the first stage of th
e phase segregation process\, in which the mixture separates into two dist
inct regions\, can be captured on the large scale by a suitable free bound
ary problem. Mykhaylo will describe the latter free boundary problem and s
ome aspects of its analysis. Jiacheng will then explain how it arises in t
he context of the Giacomin-Lebowitz model.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiacheng Zhang (Princeton)
DTSTART:20201106T203500Z
DTEND:20201106T210000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/6
DESCRIPTION:Title: A sharp interface limit in the Giacomin-Lebowitz model of phase segr
egation\nby Jiacheng Zhang (Princeton) as part of Columbia SPDE Semina
r\n\n\nAbstract\nWe will discuss the segregation process of two immiscible
substances (e.g.\, oil and water) that have been mixed together. In 1996\
, Giacomin and Lebowitz proposed a mathematical model for this process tha
t can be viewed as an alternative to the celebrated Cahn-Hilliard equation
. They also conjectured that\, in their model\, the first stage of the pha
se segregation process\, in which the mixture separates into two distinct
regions\, can be captured on the large scale by a suitable free boundary p
roblem. Mykhaylo will describe the latter free boundary problem and some a
spects of its analysis. Jiacheng will then explain how it arises in the co
ntext of the Giacomin-Lebowitz model.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Friz (TU and WIAS Berlin)
DTSTART:20201204T193000Z
DTEND:20201204T203000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/7
DESCRIPTION:Title: Laplace method on rough path and model space\nby Peter Friz (TU
and WIAS Berlin) as part of Columbia SPDE Seminar\n\n\nAbstract\nLaplace's
method allows one to obtain precise asymptotics in the large deviation pr
inciple. I will review the case of rough paths\, then talk about extension
s to rough volatility and singular SPDEs. Joint work with Paul Gassiat (Pa
ris)\, Paolo Pigato (Rom) and Tom Klose (Berlin).\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davar Khoshnevisan (Utah)
DTSTART:20200925T183000Z
DTEND:20200925T193000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/8
DESCRIPTION:Title: Ergodicity and CLT for SPDEs\nby Davar Khoshnevisan (Utah) as pa
rt of Columbia SPDE Seminar\n\n\nAbstract\nI will summarize some of the re
cent collaborative work with Le Chen\, David Nualart\, and Fei Pu in which
we characterize when the solution to a large family of parabolic stochast
ic PDE is ergodic in its spatial variable. We also identify when there are
Gaussian fluctuations associated to the resulting ergodic theorem.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Pu (Luxembourg)
DTSTART:20200925T193500Z
DTEND:20200925T200000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/9
DESCRIPTION:Title: Ergodicity and central limit theorems for parabolic Anderson model w
ith delta initial condition\nby Fei Pu (Luxembourg) as part of Columbi
a SPDE Seminar\n\n\nAbstract\nLet $\\{u(t\\\,\, x)\\}_{t >0\, x \\in\\math
bb{R}}$ denote the solution to the parabolic Anderson model with initial
condition $\\delta_0$ and driven by space-time white noise on $\\mathbb{R}
_+\\times\\mathbb{R}$\, and let $\\bm{p}_t(x):=(2\\pi t)^{-1/2}\\exp\\{-x^
2/(2t)\\}$ 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 ergodic for
every $t >0$. And we establish an associatedquantitative central limit th
eorem using Malliavin-Stein method. \nThis is based on joint work with Le
Chen\, Davar Khoshenvisan and David Nualart.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanghui Liu (Baruch College)
DTSTART:20210219T190000Z
DTEND:20210219T200000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/10
DESCRIPTION:Title: Numerical approximations for rough differential equations\nby Y
anghui Liu (Baruch College) as part of Columbia SPDE Seminar\n\n\nAbstract
\nThe rough paths theory provides a general framework for stochastic diffe
rential equations driven by processes with very low regularities\, which h
as important applications in finance\, statistical mechanics\, hydro-dynam
ics and so on. The numerical approximation is a crucial step while applyin
g these stochastic models in practice. In this talk I will introduce the r
ecent results on numerical approximation for stochastic differential equat
ions\, and then focus on the Malliavin differentiability of the Euler sche
mes. The Malliavin differentiability is a key to weak convergence and dens
ity convergence problems.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reiß (HU Berlin)
DTSTART:20210312T190000Z
DTEND:20210312T200000Z
DTSTAMP:20260422T135430Z
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\nWe shall
first discuss differences for parametric drift estimation between stochas
tic ordinary and partial differential equations (SODEs/SPDEs). For parabol
ic SPDEs a classical estimation approach is based on the spectral decompos
ition of the generator\, which is assumed to be known (at least for the ma
in symbol). For nonparametric problems this is no longer feasible. We cons
ider the specific problem of estimating the space-dependent diffusivity of
a stochastic heat equation from time-continuous observations with local s
pace resolution $h$. The rather counterintuitive result and its efficiency
as $h\\to 0$ will be discussed in detail. The methodology will be extende
d to cover more general semilinear SPDEs and an application to experimenta
l data from cell repolarisation will be presented.\n\nReferences:\nAltmeye
r\, R. and Reiß\, M. (2021)\, Nonparametric estimation for linear SPDEs f
rom local measurements\, Ann. Appl. Prob.\, to appear\, arXiv:1903.06984\n
\nAltmeyer\, R.\, Bretschneider\, T.\, Janak\, J.\, Reiß\, M. (2020) Para
meter estimation in an SPDE-model for cell repolarisation\, arXiv:2010.063
40\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Cerrai (University of Maryland)
DTSTART:20210416T180000Z
DTEND:20210416T190000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/12
DESCRIPTION:Title: On the Smoluchowski-Kramers approximation of infinite-dimensional s
ystems with state-dependent friction\nby Sandra Cerrai (University of
Maryland) as part of Columbia SPDE Seminar\n\n\nAbstract\nI will give an o
verview of a series of results on the asymptotic behavior\, with respect t
o the small mass\, of infinite-dimensional stochastic systems described by
damped waves equation perturbed by a Gaussian noise. In particular\, I wi
ll focus my attention on the case where the friction coefficient is state-
dependent.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurélien Deya (IECL\, Université de Lorraine)
DTSTART:20210423T180000Z
DTEND:20210423T190000Z
DTSTAMP:20260422T135430Z
UID:Columbia_SPDE/13
DESCRIPTION:Title: Nonlinear PDE models with stochastic fractional perturbation\nb
y Aurélien Deya (IECL\, Université de Lorraine) as part of Columbia SPDE
Seminar\n\n\nAbstract\nWe consider the following quadratic SPDE model:\n\
n$$\\mathcal{L} u= u^2+\\dot{B}\, \\quad t\\in [0\,T]\, \\\, x\\in \\math
bb{R}^d\,$$\nwhere $\\dot{B}$ is a stochastic noise\, and $\\mathcal{L}$ c
an be either: $(i)$ the heat operator $\\mathcal{L}^{\\textbf{(h)}} u=\\pa
rtial_t u-\\Delta u$\; $(ii)$ the wave operator $\\mathcal{L}^{\\textbf{(w
)}} u=\\partial^2_t u-\\Delta u$\; $(iii)$ the Schrödinger operator $\\ma
thcal{L}^{\\textbf{(s)}} u=\\imath\\partial_t u-\\Delta u$.\n\nThe dynamic
s can thus be seen\, on the one hand\, as the most basic stochastic pertur
bation of the standard nonlinear PDE $\\mathcal{L} u= u^2$\, and on the ot
her hand as the most elementary nonlinear extension of the standard SPDE $
\\mathcal{L} u= \\dot{B}$.\n\nOur objective is to study the influence of t
he roughness of $\\dot{B}$ on the equation\, and to this end\, we rely on
the great flexibility offered by the fractional noise model\n$$\\dot{B}:=\
\frac{\\partial^{d+1}B}{\\partial t\\partial x_1\\cdots \\partial x_d}\\\,
\,$$\nwhere $B$ is a space-time fractional Brownian field of indexes $H_0
\,\\ldots\,H_d\\in (0\,1)^{d+1}$.\n\nBy letting the parameters $H_i$ vary\
, we can study the transition between the regular "noiseless" situation ($
H_i\\approx 1$) and rougher common noise models: space-time white noise ($
H_i=\\frac12$)\, white-in-time noise ($H_0=\\frac12$)\, spatial noise ($H_
0\\approx 1$)\,... This gives us the opportunity to observe successive cha
nges of regimes in the handling of the equation: direct treatment\, expans
ion of higher orders\, renormalization procedures\,...\n\nWe will also dis
cuss about a first step toward the discretization of the equation above: n
amely\, the discretization of the underlying "linear" model $\\mathcal{L}
u=\\dot{B}$.\n
LOCATION:https://researchseminars.org/talk/Columbia_SPDE/13/
END:VEVENT
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