| Description |
1 online resource |
| Series |
London mathematical society lecture note series ; 436
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London Mathematical Society lecture note series ; 436.
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| Note |
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. |
| Contents |
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. |
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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. |
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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. |
| Note |
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. |
| Contents |
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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Random walks (Mathematics) -- Congresses.
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Stochastic processes -- Congresses.
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Arithmetic groups -- Congresses.
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MATHEMATICS -- Applied. |
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MATHEMATICS -- Probability & Statistics -- General. |
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Procesos estocásticos |
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Arithmetic groups |
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Random walks (Mathematics) |
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Stochastic processes |
| Genre/Form |
Conference papers and proceedings
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| Added Author |
Ceccherini-Silberstein, Tullio, editor.
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Salvatori, Maura, editor.
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Sava-Huss, Ecaterina, editor.
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Woess, Wolfgang, 1954- https://id.oclc.org/worldcat/entity/E39PBJmy3V8PPcvkydGWcCwcT3
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| Other Form: |
Print version: Groups, graphs, and random walks. Cambridge : Cambridge University Press, [2017] 9781316604403 (DLC) 2016019201 (OCoLC)948670194 |
| ISBN |
9781316818862 (electronic bk.) |
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1316818861 (electronic bk.) |
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9781316604403 |
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1316604403 |
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9781316576571 |
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1316576574 |
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