Convergence towards Burger's equation and propagation of chaos for weakly asymmetric exclusion processes

We consider a nearest neighbor exclusion process on with generator G[var epsilon] = Gs + [var epsilon]Ga, where Gs and Ga denote the generators of a symmetric and a totally asymmetric exclusion process, respectively. The parameter [var epsilon] characterizes the strength of asymmetry. In the limit as [var epsilon]-->0, we derive the law of large numbers for the associated "density field" in macroscopic space-time coordinates (corresponding to a space-time rescaling of the form x-->x/[var epsilon], t-->t/[var epsilon]2. The limiting deterministic dynamics is characterized as a solution of Burger's equation with viscosity. Furthermore, propagation of chaos is proven to hold in the macroscopic regime. Our approach is based on a non-linear transformation of the exclusion process which leads to a stochastic equation with a linear drift term.