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A central limit theorem for the KPZ equation
File | Description | Size | Format | |
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euclid.aop.1513069258.pdf | Published version | 552.58 kB | Adobe PDF | View/Open |
Title: | A central limit theorem for the KPZ equation |
Authors: | 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. |
Issue 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-ph math.AP math.MP 0104 Statistics |
Publication Status: | Published |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |