Symmetric exclusion as a random environment: invariance principle

2018/07/14 by Jara, Milton, Menezes, Otávio
#FOS: Mathematics #Primary 60K35 #Probability (math.PR) #secondary 60K37

paper · doi:10.48550/arxiv.1807.05414

Abstract

We establish an invariance principle for a one-dimensional random walk in a dynamical 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.

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