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.
Author(s): Tullio Ceccherini-Silberstein, Maura Salvatori, Ecaterina Sava-Huss
Series: London Mathematical Society Lecture Note Series 436
Publisher: Cambridge University Press
Year: 2017
Language: English
Pages: 539
Contents......Page 6
Preface......Page 8
Conference Photographs......Page 16
1 Growth of Groups and Wreath Products......Page 20
2 Random Walks on Some Countable Groups......Page 96
3 The Cost of Distinguishing Graphs......Page 123
4 A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups......Page 139
5 Structure Trees, Networks and Almost Invariant Sets......Page 156
6 Amenability of Trees......Page 195
7 Group-Walk Random Graphs......Page 209
8 Ends of Branching Random Walks on Planar Hyperbolic Cayley Graphs......Page 224
9 Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards......Page 234
10 Schreier Graphs of Grigorchuk’s Group and a Subshift Associated to a Nonprimitive Substitution......Page 269
11 Thompson’s Group F is Not Liouville......Page 319
12 A Proof of the Subadditive Ergodic Theorem......Page 362
13 Boundaries of Zn -Free Groups......Page 374
14 Buildings, Groups of Lie Type and Random Walks......Page 410
15 On Some Random Walks Driven by Spread-Out Measures......Page 463
16 Topics on Mathematical Crystallography......Page 494
