## Electronic Communications in Probability

### Mixing time for the random walk on the range of the random walk on tori

#### 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 $1 - Ce^{-(\log N)^2}$.

#### Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 26, 10 pp.

Dates
Accepted: 4 March 2016
First available in Project Euclid: 10 March 2016

https://projecteuclid.org/euclid.ecp/1457617917

Digital Object Identifier
doi:10.1214/16-ECP4750

Mathematical Reviews number (MathSciNet)
MR3485395

Zentralblatt MATH identifier
1338.60240

#### Citation

Černý, Jiří; Sapozhnikov, Artem. Mixing time for the random walk on the range of the random walk on tori. Electron. Commun. Probab. 21 (2016), paper no. 26, 10 pp. doi:10.1214/16-ECP4750. https://projecteuclid.org/euclid.ecp/1457617917

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