A STOCHASTIC BURGERS EQUATION FROM A CLASS OF MICROSCOPIC INTERACTIONS

• 成果类型: Article
• 署名作者: Goncalves, Patricia; Jara, Milton; Sethuraman, Sunder
• 署名单位: Universidade do Minho; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Arizona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP878
• 发表日期: 2015
• 页码: 286-338
• 关键词: asymmetric simple exclusion; central-limit-theorem; zero-range process; symmetric simple exclusion; particle-systems; spectral gap; equilibrium fluctuations; tagged particle; kpz equation; growth-model

摘要

We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on 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 <= 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 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.