Groups, Graphs and Random Walks
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Groups, Graphs and Random Walks
About this book
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; Schrödinger 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.
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Information
Table of contents
- Cover
- Series information
- Title page
- Copyright information
- Table of contents
- Preface
- Conference Photographs
- 1 Growth of Groups and Wreath Products
- 2 Random Walks on Some Countable Groups
- 3 The Cost of Distinguishing Graphs
- 4 A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups
- 5 Structure Trees, Networks and AlmostInvariant Sets
- 6 Amenability of Trees
- 7 Group-Walk Random Graphs
- 8 Ends of Branching Random Walks on Planar Hyperbolic Cayley Graphs
- 9 Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards
- 10 Schreier Graphs of Grigorchuk's Group and a Subshift Associated to a Nonprimitive Substitution
- 11 Thompson's Group F is Not Liouville
- 12 A Proof of the Subadditive Ergodic Theorem
- 13 Boundaries of mathbb Z[sup(n)]-Free Groups
- 14 Buildings, Groups of Lie Type and Random Walks
- 15 On Some Random Walks Driven by Spread-Out Measures
- 16 Topics on Mathematical Crystallography