Symmetric exclusion as a random environment: Invariance principle

Abstract

We establish an invariance principle for a one-dimensional random walk in a dynamic random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes: a Brownian motion and a Gaussian process with stationary increments.