Scaling limits of Wick ordered KPZ equation
type: Item
instance of: scholarly article
title: Scaling limits of Wick ordered KPZ equation
zbMATH Open document ID: 0956.60077
DOI: 10.1007/PL00020963
author: Terence Chan
published in: Communications in Mathematical Physics
publication date: 2001-03-02T00:00:00Z
review text: The author considers the Kardar-Parisi-Zhang (KPZ) equation [Phys. Rev. Lett. 56, 889-892 (1984)], which is \[ \frac{\partial u}{\partial t}=\nu\Delta u+\frac{\lambda}{2}|\nabla u|^2+\sigma W(t,x),\qquad u(0,x)=u_0(x), \] where \(W(t,x)\) is a space-time white noise, \(u=u(t,x)\) and \(x\in \mathbb{R}^d\). The paper investigates the convergence of rescaled functions of the form \(k^{-\chi}u(k^zt,kx)\), as \(k\to\infty\), for some exponents \(\chi\) and \(z\). This problem is solved for various values of \(\chi\) and \(z\) (depending on the dimension \(d\)) using the Wiener chaos expansion and the tools of white noise analysis.
Mathematics Subject Classification ID: 60H40
zbMATH DE Number: 1422935
zbMATH Keywords: white noise
zbMATH Keywords: Wiener chaos expansion
reviewed by: Rolando Rebolledo
MaRDI profile type: Publication
full work available at URL: pl00020963
OpenAlex ID: W2002502603
description: scientific article; zbMATH DE number 1422935