A stochastic Burgers equation from a class of microscopic interactions

ABSTRACT. 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−γ) for 1/2 < γ ≤ 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 γ = 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. 1