Reversible random walks on dynamic graphs

Abstract

AbstractThis paper discusses random walks on edge‐changing dynamic graphs. We prove general and improved bounds for mixing, hitting, and cover times for a random walk according to a sequence of irreducible and reversible transition matrices with the time‐invariant stationary distribution. An interesting consequence is the tight bounds of the lazy Metropolis walk on any dynamic connected graph. We also prove bounds for multiple random walks on dynamic graphs. Our results extend previous upper bounds for simple random walks on dynamic graphs and give improved and tight upper bounds in several cases. Our results reinforce the observation that time‐inhomogeneous Markov chains with an invariant stationary distribution behave almost identically to a time‐homogeneous chain.