Open Access
November 2020 A comparison principle for random walk on dynamical percolation
Jonathan Hermon, Perla Sousi
Ann. Probab. 48(6): 2952-2987 (November 2020). DOI: 10.1214/20-AOP1441


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.


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Jonathan Hermon. Perla Sousi. "A comparison principle for random walk on dynamical percolation." Ann. Probab. 48 (6) 2952 - 2987, November 2020.


Received: 1 April 2019; Revised: 1 January 2020; Published: November 2020
First available in Project Euclid: 20 October 2020

MathSciNet: MR4164458
Digital Object Identifier: 10.1214/20-AOP1441

Primary: 60F05 , 60G50

Keywords: Dynamical percolation , hitting times , Mixing times , spectral profile

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 6 • November 2020
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