Title Groups, graphs, and random walks / edited by Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Maura Salvatori, Università degli Studi di Milano, Ecaterina Sava-Huss, Cornell University, New York

Published Cambridge : Cambridge University Press, [2017]

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Description 1 online resource Series London mathematical society lecture note series ; 436 London Mathematical Society lecture note series ; 436. Contents 880-01 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 880-01/(S AcknowledgmentReferences; Added in Proof; 4 A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups; 1. G-Harmonic Functions and G-Poisson Boundary; 2. From Γ-Boundaries to G-Boundaries; 3. G-Poisson Boundary of Baumslag-Solitar Group; References; 5 Structure Trees, Networks and AlmostInvariant Sets; 1. Introduction; 2. Networks and Structure Trees; 2.1. Finite Networks; 2.2. The Algebra of Cuts; 2.3. Flows in Networks; 3. Almost Invariant Sets; 3.1. Relative Structure Trees; 4. H-Almost Stability; References; 6 Amenability of Trees; Introduction 7.2. Finite-Valued Permutational Wreath Products7.3. Imbedding in the Derived Subgroup; 7.4. Spreading, Stabilizing, Rectifiable Sequences; 7.5. Subexponential Growth of Wreath Products; 8. Groups of Non-Uniform Exponential Growth; References; 2 Random Walks on Some Countable Groups; 1. Introduction; 1.1. Union of Finite Groups; 1.2. Direct Sums; 1.3. Other Examples; 2. Selected Technical Tools; 3. Random Walks on Increasing Union of Finite Groups; 3.1. On Diagonal Upper Bounds: Convex Combinations of Commuting Probability Densities 3.2. On Diagonal Bounds: Convex Combinations of Haar Measures and Comparison4. Examples on mathbb S[sup((∞))] ; 4.1. Behavior of Convex Combinations of Uniforms; 4.2. Walks Based on Small Generating Sets of mathbb S[sub(n)] ; 5. Around the Recurrence/Transience Dichotomy; 6. Direct Sums of Finitely Generated Groups; 6.1. Examples on Direct Sums; 6.2. Comparison Inequalities; References; 3 The Cost of Distinguishing Graphs; 1. Introduction; 2. Preliminaries; 3. Finite Graphs; 4. Infinite Graphs; 4.1. A New Bound for Linear Growth; 4.2. Graphs with Two Ends; 4.3. The Main Result; 5. Outlook Summary An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields Notes Based on the workshop "Groups, Graphs and Random Walks," held in Cortona, Italy, on June 2-6, 2014, on the occasion of the 60th birthday of Wolfgang Woess Bibliography Includes bibliographical references and index Notes 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 Print version record Subject Random walks (Mathematics) -- Congresses Stochastic processes -- Congresses Arithmetic groups -- Congresses MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Procesos estocásticos Arithmetic groups Random walks (Mathematics) Stochastic processes Genre/Form Conference papers and proceedings Form Electronic book Author Ceccherini-Silberstein, Tullio, editor. Salvatori, Maura, editor. Sava-Huss, Ecaterina, editor. Woess, Wolfgang, 1954- ISBN 9781316818862 1316818861 9781316576571 1316576574

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