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A comparison principle for random walk on dynamical percolation

2020; Institute of Mathematical Statistics; Volume: 48; Issue: 6 Linguagem: Inglês

10.1214/20-aop1441

2168-894X

Jonathan Hermon, Perla Sousi,

Random Matrices and Applications

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.