An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schr�dinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.

About the Authors

Tullio Ceccherini-Silberstein is a professor in the Department of Engineering at Universit� del Sannio (Benevento), Italy.

Maura Salvatori is an associate professor in the Department of Mathematics at Universit� degli Studi di Milano, Italy.

Ecaterina Sava-Huss is a visiting assistant professor in the Department of Mathematics at Cornell University, New York.

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