A stochastic Burgers equation from a class of microscopic interactions

• Author(s): Gonçalves, Patrícia ; Jara, Milton ; Sethuraman, Sunder
• Date: 2013
• Persistent ID: http://hdl.handle.net/1822/24264
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): KPZ equation; Burgers; Weakly asymmetric; Zero-range; Kinetically constrained; Equilibrium fluctuations; Speed-change; Fluctuations
• Document Type: Preprint
• Language: English

Description

Documento submetido para revisão pelos pares. A publicar em Annals of Probability. ISSN 0091-1798 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 $1/2<\gamma\leq 1$, 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.