Variable speed symmetric random walk driven by symmetric exclusion

2021/07/17 by Otávio Menezes, Menezes, Otávio, Jonathon Peterson +3
Mathematics · Physics and Astronomy · #60F17 #60K35 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2107.08235

openalex publication_date 2021/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.

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