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2017 Cutoff for Ramanujan graphs via degree inflation
Jonathan Hermon
Electron. Commun. Probab. 22(none): 1-10 (2017). DOI: 10.1214/17-ECP72

Abstract

Recently Lubetzky and Peres showed that simple random walks on a sequence of $d$-regular Ramanujan graphs $G_n=(V_n,E_n)$ of increasing sizes exhibit cutoff in total variation around the diameter lower bound $\frac{d} {d-2}\log _{d-1}|V_n| $. We provide a different argument under the assumption that for some $r(n) \gg 1$ the maximal number of simple cycles in a ball of radius $r(n)$ in $G_n$ is uniformly bounded in $n$.

Citation

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Jonathan Hermon. "Cutoff for Ramanujan graphs via degree inflation." Electron. Commun. Probab. 22 1 - 10, 2017. https://doi.org/10.1214/17-ECP72

Information

Received: 26 February 2017; Accepted: 5 July 2017; Published: 2017
First available in Project Euclid: 15 August 2017

zbMATH: 1378.05188
MathSciNet: MR3693771
Digital Object Identifier: 10.1214/17-ECP72

Subjects:
Primary: 05C12, 05C81, 60B10, 60J10

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