Unimodularity in randomly generated graphs /

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 gr...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Sobieczky, Florian (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2018.
Colección:Contemporary mathematics (American Mathematical Society) ; v. 719.
Temas:
Random graphs.
Graph theory.
Graphes aléatoires.
MATHEMATICS > Applied.
MATHEMATICS > Probability & Statistics > General.
Graph theory
Random graphs
Probability theory and stochastic processes > Special processes > Interacting random processes; statistical mechanics type models; percolation theory.
Probability theory and stochastic processes > Special processes > Processes in random environments.
Probability theory and stochastic processes > Markov processes > Transition functions, generators and resolvents.
Probability theory and stochastic processes > Combinatorial probability > Combinatorial probability.
Probability theory and stochastic processes > Stochastic processes > Point processes.
Dynamical systems and ergodic theory > Ergodic theory > Measure-preserving transformations.
Dynamical systems and ergodic theory > Ergodic theory > Entropy and other invariants, isomorphism, classification.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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
  • 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
  • 7. Proofs8. Bibliography of Analogous Results for Point Processes; Acknowledgements; References; Back Cover

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