A stochastic Burgers equation from a class of microscopic interactions
Abstract
We consider a class of nearestneighbor weakly asymmetric mass conservative particle systems evolving on $\mathbb{Z}$, which includes zerorange 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 OrnsteinUhlenbeck 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 "BoltzmannGibbs" estimate which improves on earlier bounds.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1210.0017
 Bibcode:
 2012arXiv1210.0017G
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 Published in at http://dx.doi.org/10.1214/13AOP878 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)