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01 October 2020
  » arxiv » 1210.0017

 Article overview

A stochastic Burgers equation from a class of microscopic interactions
Patricia Goncalves ; Milton Jara ; Sunder Sethuraman ;
Date 28 Sep 2012
AbstractWe consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order $O(n^{-gamma})$ for $1/2<gammaleq 1$, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when $gamma = 1/2$, we show that all limit points solve a martingale problem which may be interpreted in terms of a stochastic Burgers equation derived from taking the gradient of the KPZ equation. The proofs make use of a sharp ’Boltzmann-Gibbs’ estimate which improves on earlier bounds.
Source arXiv, 1210.0017
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