Coarse geometry and randomness: École d'Été de Probabilités de Saint-Flour XLI - 2011 / Itai Benjamini

Collectivité principale: école d'été de probabilités de Saint-Flour, 41, Saint-Flour (2011) Auteur secondaire : Benjamini, Itai - Editeur scientifiqueType de document: Livre numériqueCollection: Lecture notes in mathematics ; 2100Langue: anglaisÉditeur: New York : Springer, cop. 2013 ISBN: 9783319025759 Note: From the preface: "The first part of the notes reviews several coarse geometric concepts. We will then move on and look at the manifestation of the underling geometry in the behavior of random processes, mostly percolation and random walk. "The study of the geometry of infinite vertex transitive graphs and Cayley graphs in particular is rather well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic. That is, admitting a combination of properties not encountered in the vertex transitive world. These include percolation cluster on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation. "Chapter 5 is due to Nicolas Curien, Chap. 12 was written by Ariel Yadin, and Chap. 13 is joint work with Gady Kozma.'' Sujets MSC: 05C10 Combinatorics -- Graph theory -- Planar graphs; geometric and topological aspects of graph theory
05C80 Combinatorics -- Graph theory -- Random graphs
05C81 Combinatorics -- Graph theory -- Random walks on graphs
82B41 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Random walks, random surfaces, lattice animals, etc
82B43 Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Percolation
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From the preface: "The first part of the notes reviews several coarse geometric concepts. We will then move on and look at the manifestation of the underling geometry in the behavior of random processes, mostly percolation and random walk.
"The study of the geometry of infinite vertex transitive graphs and Cayley graphs in particular is rather well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic. That is, admitting a combination of properties not encountered in the vertex transitive world. These include percolation cluster on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation.
"Chapter 5 is due to Nicolas Curien, Chap. 12 was written by Ariel Yadin, and Chap. 13 is joint work with Gady Kozma.''

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