Wolfgang Woess, "Random Walks on Infinite Graphs and Groups"  
Cambridge University Press | 2000 | ISBN: [url=]0521552923[/url] | 348 pages |

Thiseminent work focuses on the interplay between the behavior of randomwalks and discrete structure theory. Wolfgang Woess considers Markovchains whose state space is equipped with the structure of an infinite,locally-finite graph, or of a finitely generated group. He assumes thetransition probabilities are adapted to the underlying structure insome way that must be specified precisely in each case. He alsoexplores the impact the particular type of structure has on variousaspects of the behavior of the random walk. In addition, the authorshows how random walks are useful tools for classifying, or at leastdescribing, the structure of graphs and groups.