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 viewp…
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- Full title :Random walks on infinite graphs and groups / Wolfgang Woess.
Summary
"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. Conversely, random walks may also be seen as a useful tool 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 for all researchers working in stochastic processes and related topics."--Jacket.
Read More ↓Edition Statements
- Publication Date:2000.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2000.
Notes
Bibliographic Level Mode of Issuance: Monograph.
The Physical Object
- Description:1 online resource (xi, 334 p. ) : ill.
Edition Identifiers
- ISBN:0511470967, 9780511470967
- oclc:on1242476878
- LC Classification:QA274.73
- Dewey Decimal:519.2/82
Table of Contents
Ch. I. The type problem -- Ch. II. The spectral radius -- Ch. III. The asymptotic behaviour of transition probabilities -- Ch. IV. An introduction to topological boundary theory.
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