| Description |
1 online resource (x, 211 pages) |
| Series |
Contemporary mathematics ; volume 719 |
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Contemporary mathematics (American Mathematical Society) ; v. 719.
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| Contents |
Cover; Title page; Contents; Preface; Monotonicity of average return probabilities for random walks in random environments; 1. Introduction; 2. Statements of Results and Background; 3. Proofs; References; Counterexamples for percolation on unimodular random graphs; 1. Introduction; 2. Basic constructions; 3. A discontinuous phase transition; 4. Nonamenability and uniqueness; References; Invariant -percolation on regular trees; References; Sparse graph limits along balls; 1. Hyperfiniteness; 2. Yu's Property; 3. Further questions that arise; 4. An infinite model; References |
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Percolation and coarse conformal uniformization1. Introduction; 2. Two conjectures; 3. Conformal invariance and hyperbolicity; References; Invariant tilings and unimodular decorations of Cayley graphs; 1. Introduction; 2. Duality; References; Distributional lattices on Riemannian symmetric spaces; 1. Introduction; 2. Distributional lattices; 3. General Properties of Poisson-Voronoi tilings in Symmetric Spaces; 4. Additional structure for Poisson-Voronoi tessellations in nonpositively curved spaces; References; Eternal Family Trees and dynamics on unimodular random graphs; 1. Introduction |
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2. Unimodular Networks3. Vertex-Shifts and Foil Classification; 4. Eternal Family Trees; 5. Trees and Networks Beyond Unimodularity; 6. Eternal Branching Processes; Conclusion; Acknowledgements; References; Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders; Introduction; 1. De Bruijn graphs; 2. Circular slider graphs; 3. Examples; 4. Periodic slider graphs: connectedness and step induced graphs; 5. Missing links and transversally Markov circular slider graphs; 6. Lamplighters over cyclic groups; 7. Lamplighters and circular slider graphs; 8. Spider slider graphs |
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7. Proofs8. Bibliography of Analogous Results for Point Processes; Acknowledgements; References; Back Cover |
| Summary |
This volume contains the proceedings of the AMS Special Session on Unimodularity in Randomly Generated Graphs, held from October 8-9, 2016, in Denver, Colorado. Unimodularity, a term initially used in locally compact topological groups, is one of the main examples in which the generalization from groups to graphs is successful. The "randomly generated graphs", which include percolation graphs, random Erdős-Rényi graphs, and graphings of equivalence relations, are much easier to describe if they result as random objects in the context of unimodularity, with respect to either a vertex-transien |
| Notes |
"AMS Special Session on Unimodularity in Randomly Generated Graphs, October 8-9, 2016, Denver, Colorado." |
| Bibliography |
Includes bibliographical references |
| Notes |
Print record version |
| Subject |
Random graphs.
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Graph theory.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Graph theory
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Random graphs
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Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory.
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Probability theory and stochastic processes -- Special processes -- Processes in random environments.
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Probability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolvents.
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Probability theory and stochastic processes -- Combinatorial probability -- Combinatorial probability.
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Probability theory and stochastic processes -- Stochastic processes -- Point processes.
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Dynamical systems and ergodic theory -- Ergodic theory -- Measure-preserving transformations.
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Dynamical systems and ergodic theory -- Ergodic theory -- Entropy and other invariants, isomorphism, classification.
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| Form |
Electronic book
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| Author |
Sobieczky, Florian, editor.
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| ISBN |
1470450178 |
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9781470450175 |
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