A COMPARISON PRINCIPLE FOR RANDOM WALK ON DYNAMICAL PERCOLATION

• 成果类型: Article
• 署名作者: Hermon, Jonathan; Sousi, Perla
• 署名单位: University of British Columbia; University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1441
• 发表日期: 2020
• 页码: 2952-2987
• 关键词: mixing times; inequalities; bounds

摘要

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 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.