Random Walks on Infinite 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. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. 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. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Reviews & endorsements

Review of the hardback: 'This is an excellent book, where beginners and specialists alike will find useful information. It will become one of the major references for all those interested directly or indirectly in random walks. I highly recommend it.' L. Saloff-Coste, Bulletin of the London Mathematical Society

Customer reviews

Product details

• Date Published: May 2008
• format: Paperback
• isbn: 9780521061728
• length: 352 pages

• dimensions: 229 x 152 x 20 mm
• weight: 0.52kg
• contains: 12 b/w illus.
• availability: Available