Coarse geometry and randomness [Documento electrónico] : école d’Été de probabilités de Saint-Flour XLI – 2011 / Itai Benjamini
Language: eng.Country: Germany.Publication: Cham : Springer International Publishing, 2013Description: VII, 129 p. : il.ISBN: 978-3-319-02576-6.Series: Lecture Notes in MathematicsSubject - Topical Name: Processos estocásticos | Passeios aleatórios (Matemática) Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA274.SPR FCT 81815 Stochastic world | QA274.SPR FCT 81851 Discrete–time stochastic control and dynamic potential games, the Euler–equation approach | QA274.SPR FCT 81862 Optimal stochastic control schemes within a structural reliability framework | QA274.SPR FCT 81908 Coarse geometry and randomness, école d’Été de probabilités de Saint-Flour XLI – 2011 | QA274.SPR FCT 81933 Modern stochastics and applications | QA274.SPR FCT 82084 Multistage stochastic optimization | QA274.SPR FCT 82136 Stochastic processes , inference theory |
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These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly 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, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters 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 (SHIQ).
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