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The L2-cutoffs for reversible Markov chains

2017/01/23 by Guan‐Yu Chen, Chen, Guan-Yu, Jui‐Ming Hsu +3
Mathematics · Physics and Astronomy · #60J10 #60J27 #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1701.06663

openalex publication_date 2017/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we considers reversible Markov chains of which L2-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [8], while we provide here a completely different pathway to analyze the L2-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between discrete time lazy chains and continuous time chains. For an illustration, we consider product chains, a rather complicated model which could be involved to analyze using the method in [8], and derive the equivalence of their L2-cutoffs.

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