Bounds on Mixing Time for Time-Inhomogeneous Markov Chains

2023/09/26 by Raphael Erb, Erb, Raphael
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #Genetic Syndromes and Imprinting #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2309.14790

openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end, we propose a concept of mixing time for time-inhomogeneous Markov chains. We then develop techniques to estimate this mixing time by extending the evolving set method of Morris and Peres (2003). We apply these techniques to study a random walk on a dynamic Erdős-Rényi graph, proving that the mixing time is O(log(n)) when the graph is well above the connectivity threshold. We also give an almost matching lower bound.

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