Overview
- Includes many exercises of varying difficulty levels
- Investigates many open problems
- Presents topics not covered by any other book
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2100)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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).
Authors and Affiliations
Bibliographic Information
Book Title: Coarse Geometry and Randomness
Book Subtitle: École d’Été de Probabilités de Saint-Flour XLI – 2011
Authors: Itai Benjamini
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-02576-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-02575-9Published: 19 December 2013
eBook ISBN: 978-3-319-02576-6Published: 02 December 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VII, 129
Number of Illustrations: 3 b/w illustrations, 3 illustrations in colour
Topics: Geometry, Probability Theory and Stochastic Processes, Mathematical Methods in Physics, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Solid Mechanics, Graph Theory