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arXiv · 2009.00837

An entropic proof of cutoff on Ramanujan graphs

Narutaka Ozawa
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Abstract

It is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon, that is to say, the total variation distance of the random walk distribution from the uniform distribution drops abruptly from near $1$ to near $0$. There are already a few alternative proofs of this fact. In this note, we give yet another proof based on functional analysis and entropic consideration.

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Narutaka Ozawa. 2020-09-02. An entropic proof of cutoff on Ramanujan graphs. https://arxiv.org/abs/2009.00837

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