Transient random walk in symmetric exclusion: limit theorems and an Einstein relation

2011/02/05 by Luca Avena, Avena, Luca, Renato dos Santos +3
Mathematics · #60K37 (Primary) 60Fxx #82C22 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1102.1075

openalex publication_date 2011/02/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We construct a renewal structure from which a LLN, a functional CLT and large deviation bounds for the random walk under the annealed measure follow. We further prove an Einstein relation under a suitable perturbation. A brief discussion on the topic of random walks in slowly mixing dynamic random environments is presented.

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