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  3. Random Walks on Infinite Graphs and Groups
  • Cited by 467
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
2000
Online ISBN:
9780511470967
DOI:
https://doi.org/10.1017/CBO9780511470967
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Tracts in Mathematics (138)
Information

Book description

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

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 Source: Bulletin of the London Mathematical Society

Review of the hardback:‘… will be essential reading for all researchers in stochastic processes and related topics.’

Source: European Maths Society Journal

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