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Coarse Geometry and Randomness - Ecole d'Ete de Probabilites de Saint-Flour XLI - 2011 (Paperback, 2013 ed.)
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Coarse Geometry and Randomness - Ecole d'Ete de Probabilites de Saint-Flour XLI - 2011 (Paperback, 2013 ed.)
Series: Lecture Notes in Mathematics, 2100
Expected to ship within 10 - 15 working days
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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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