A central limit theorem for the KPZ equation

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Title: A central limit theorem for the KPZ equation
Author(s): Hairer, M
Shen, H
Item Type: Journal Article
Abstract: We consider the KPZ equation in one space dimension driven by a stationary centred space–time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the Hopf–Cole solution to the KPZ equation driven by space–time Gaussian white noise. While the limiting process depends only on the integrated variance of the driving field, the diverging constants appearing in the definition of the reference frame also depend on higher order moments.
Publication Date: 12-Dec-2017
Date of Acceptance: 1-Aug-2016
URI: http://hdl.handle.net/10044/1/57636
DOI: https://dx.doi.org/10.1214/16-AOP1162
ISSN: 0091-1798
Publisher: Institute of Mathematical Statistics
Start Page: 4167
End Page: 4221
Journal / Book Title: Annals of Probability
Volume: 45
Issue: 6B
Copyright Statement: © Institute of Mathematical Statistics, 2017
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
KPZ equation
central limit theorem
Wiener chaos
cumulants
REGULARITY STRUCTURES
PARTICLE-SYSTEMS
RENORMALIZATION
math.PR
math.PR
math-ph
math.AP
math.MP
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
KPZ equation
central limit theorem
Wiener chaos
cumulants
REGULARITY STRUCTURES
PARTICLE-SYSTEMS
RENORMALIZATION
0104 Statistics
Statistics & Probability
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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