%0 Journal Article
%T A stochastic Burgers equation from a class of microscopic interactions
%A Patr¨ªcia Gon£¿alves
%A Milton Jara
%A Sunder Sethuraman
%J Mathematics
%D 2012
%I arXiv
%R 10.1214/13-AOP878
%X We 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 $1/2<\gamma\leq1$, 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 satisfy a martingale formulation 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.
%U http://arxiv.org/abs/1210.0017v2