Random Walks on Infinite Graphs and Groups (Cambridge Tracts in Mathematics, Series Number 138)

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.

The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. This book will be essential reading for all researchers working in stochastic process and related topics.