On the time taken by random walks on finite groups to visit every state

Abstract

Consider a random walk on a finite group G. Suppose that the time taken for the transition probabilities to approach the uniform distribution is small compared with #G. Then the time taken for the random walk to visit every state is approximately R#G·log(#G), where R is the mean number of returns to the initial state in the short term. © 1983 Springer-Verlag.