INTERFACE FLUCTUATIONS IN THE 2-DIMENSIONAL WEAKLY ASYMMETRIC SIMPLE EXCLUSION PROCESS

[摘要] We consider the two-dimensional weakly asymmetric simple exclusion process, where the asymmetry is along the X-axis. The generator for such a process can be written as epsilon-2L0 + epsilon-1L(alpha), epsilon > 0, where L0 and L(alpha) are the generators for the nearest neighbor symmetric simple exclusion and totally asymmetric simple exclusion, respectively. We prove propagation of chaos and convergence to Burgers equation with viscosity in the limit as epsilon goes to zero. ne density fluctuation field converges to a generalized Ornstein-Uhlenbeck process. The covariance kernel for a class of travelling wave solutions is consistent with a phase boundary which fluctuates according to a linear stochastic partial differential equation.

[发布日期] 1992-12-01

[关键词] INFINITE PARTICLE SYSTEMS;SIMPLE EXCLUSION;BURGERS EQUATION;ORNSTEIN-UHLENBECK PROCESS