Remarks on cutoff phenomena for random walks on Hamming Schemes

Abstract

The sequence of the simple random walks on Hamming schemes $\{H(n,q){\}}_{n=1}^{\infty }$ 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 $\{H(n,q){\}}_{n=1}^{\infty }$ with $q\ge 3$, we give a simple majorant and a sharp minorant function for total variance distances between transition distributions and stationary distributions.

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• Finite Gelfand Pair Approaches for Ehrenfest Diffusion Model
• Interactions between Ehrenfest's urns arising from group actions