Remarks on cutoff phenomena for random walks on Hamming Schemes

2016/01/14 by Katsuhiko Kikuchi, Kikuchi, Katsuhiko
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1601.03548

openalex publication_date 2016/01/14 · arxiv created 2016/02/09 · arxiv updated 2016/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The sequence of the simple random walks on Hamming schemes \H(n, q)\_n=1^∞ has a cutoff phenomenon for each integer q greater than or equal to 3. In this paper, for the sequence of simple random walks on Hamming schemes \H(n, q)\_n=1^∞ with q≥ 3, we give a simple majorant and a sharp minorant function for total variance distances between transition distributions and stationary distributions.

Citations

• Finite Gelfand Pair Approaches for Ehrenfest Diffusion Model

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