Cutoff for activated random walk

2025/01/29 by Christopher Hoffman, Tobias Johnson, Hoffman, Christopher +4 · 2 citations
Computer Science · Mathematics · #37A25 #60J10 #60K35 #82C22 #FOS: Mathematics #FOS: Physical sciences #Formal Methods in Verification #Machine Learning and Algorithms #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2501.17938

openalex publication_date 2025/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the mixing time of driven-dissipative activated random walk on an interval of length n with uniform or central driving exhibits cutoff at n times the critical density for activated random walk on the integers. The proof uses a new result for arbitrary graphs showing that the chain is mixed once activity is likely at every site.

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