## Annals of Probability

### A comparison principle for random walk on dynamical percolation

#### Abstract

We consider the model of random walk on dynamical percolation introduced by Peres, Stauffer and Steif in (Probab. Theory Related Fields 162 (2015) 487–530). We obtain comparison results for this model for hitting and mixing times and for the spectral gap and log-Sobolev constant with the corresponding quantities for simple random walk on the underlying graph $G$, for general graphs. When $G$ is the torus $\mathbb{Z}_{n}^{d}$, we recover the results of Peres et al., and we also extend them to the critical case. We also obtain bounds in the cases where $G$ is a transitive graph of moderate growth and also when it is the hypercube.

#### Article information

Source
Ann. Probab., Volume 48, Number 6 (2020), 2952-2987.

Dates
Revised: January 2020
First available in Project Euclid: 20 October 2020

Permanent link to this document
https://projecteuclid.org/euclid.aop/1603180870

Digital Object Identifier
doi:10.1214/20-AOP1441

Mathematical Reviews number (MathSciNet)
MR4164458

#### Citation

Hermon, Jonathan; Sousi, Perla. A comparison principle for random walk on dynamical percolation. Ann. Probab. 48 (2020), no. 6, 2952--2987. doi:10.1214/20-AOP1441. https://projecteuclid.org/euclid.aop/1603180870

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