Speed of random walk on dynamical percolation in nonamenable transitive graphs

2024/07/21 by Chenlin Gu, Jianping Jiang, Gu, Chenlin +9 · 1 citation
Physics and Astronomy · Mathematics · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.2407.15079

Abstract

Let G be a nonamenable transitive unimodular graph. In dynamical percolation, every edge in G refreshes its status at rate μ>0, and following the refresh, each edge is open independently with probability p. The random walk traverses G only along open edges, moving at rate 1. In the critical regime p=p_c, we prove that the speed of the random walk is at most O(√(μlog(1/μ))), provided that μ≤ e^-1. In the supercritical regime p>p_c, we prove that the speed on G is of order 1 (uniformly in μ), while in the subcritical regime p

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