Random Walks on Infinite Graphs and Groups

This eminent work focuses on the interplay between the behavior of random walks and discrete structure theory. Wolfgang Woess considers Markov chains whose state space is equipped with the structure of an infinite locally-finite graph or of a finitely generated group. He assumes the transition probabilities are adapted to the underlying structure in some way that must be specified precisely in each case. He also explores the impact the particular type of structure has on various aspects of the behavior of the random walk. In addition the author shows how random walks are useful tools for classifying or at least describing the structure of graphs and groups.