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2020 An entropic proof of cutoff on Ramanujan graphs
Narutaka Ozawa
Electron. Commun. Probab. 25: 1-8 (2020). DOI: 10.1214/20-ECP358

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.

Citation

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Narutaka Ozawa. "An entropic proof of cutoff on Ramanujan graphs." Electron. Commun. Probab. 25 1 - 8, 2020. https://doi.org/10.1214/20-ECP358

Information

Received: 7 September 2020; Accepted: 2 November 2020; Published: 2020
First available in Project Euclid: 10 November 2020

MathSciNet: MR4178418
Digital Object Identifier: 10.1214/20-ECP358

Subjects:
Primary: 05C81, 60J10, 94A17

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