Annals of Probability

A comparison principle for random walk on dynamical percolation

Jonathan Hermon and Perla Sousi

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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

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

Received: April 2019
Revised: January 2020
First available in Project Euclid: 20 October 2020

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Mathematical Reviews number (MathSciNet)

Primary: 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks

Dynamical percolation mixing times hitting times spectral profile


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.

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