Groups, graphs and random walks

✍ Scribed by Ceccherini-Silberstein, Tullio; Salvatori, Maura; Sava-Huss, Ecaterina; Woess, Wolfgang (ed.)

• Publisher: Cambridge University Press
• Year: 2017
• Tongue: English
• Leaves: 539
• Series: London mathematical society lecture notes 436
• Category: Library

✦ Synopsis

An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.;Cover; Series information ; Title page ; Copyright information ; Table of contents ; Preface; Conference Photographs; 1 Growth of Groups and Wreath Products; Introduction; 1. Wreath Products; 1.1. Actions; 1.2. History; 1.3. Generators for Wreath Products; 2. Growth of Groups; 2.1. Formal Growth; 2.2. Complete Growth Series; 2.3. Asymptotic Growth; 2.4. History; 3. Growth of Regular Wreath Products; 3.1. Wreath Products Over Finite Sets; 3.2. Lamplighter Groups; 3.3. Regular Wreath Products with Free Groups; 3.4. Travelling Salesmen; 3.5. Asymptotic Growth; 4. (Self- )similar Groups.

✦ Table of Contents

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

✦ Subjects

Arithmetic groups;MATHEMATICS--Applied;MATHEMATICS--Probability & Statistics--General;Random walks (Mathematics);Stochastic processes;Conference papers and proceedings;Electronic books;Conference publication;Random walks (Mathematics) -- Congresses;Stochastic processes -- Congresses;Arithmetic groups -- Congresses;MATHEMATICS -- Applied;MATHEMATICS -- Probability & Statistics -- General