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2016 Mixing time for the random walk on the range of the random walk on tori
Jiří Černý, Artem Sapozhnikov
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP4750

Abstract

Consider the subgraph of the discrete $d$-dimensional torus of size length $N$, $d\geq 3$, induced by the range of the simple random walk on the torus run until the time $uN^d$. We prove that for all $d\geq 3$ and $u>0$, the mixing time for the random walk on this subgraph is of order $N^2$ with probability at least $1 - Ce^{-(\log N)^2}$.

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Jiří Černý. Artem Sapozhnikov. "Mixing time for the random walk on the range of the random walk on tori." Electron. Commun. Probab. 21 1 - 10, 2016. https://doi.org/10.1214/16-ECP4750

Information

Received: 15 December 2015; Accepted: 4 March 2016; Published: 2016
First available in Project Euclid: 10 March 2016

zbMATH: 1338.60240
MathSciNet: MR3485395
Digital Object Identifier: 10.1214/16-ECP4750

Subjects:
Primary: 58J35, 60K37

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