École d'Été de Probabilités de Saint-Flour

Coarse Geometry and Randomness

École d’Été de Probabilités de Saint-Flour XLI – 2011

Authors: Benjamini, Itai

  • Includes many exercises of varying difficulty levels
  • Investigates many open problems
  • Presents topics not covered by any other book
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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).

Table of contents (13 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02576-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-02575-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Coarse Geometry and Randomness
Book Subtitle
École d’Été de Probabilités de Saint-Flour XLI – 2011
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2100
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02576-6
DOI
10.1007/978-3-319-02576-6
Softcover ISBN
978-3-319-02575-9
Series ISSN
0721-5363
Edition Number
1
Number of Pages
VII, 129
Number of Illustrations and Tables
3 b/w illustrations, 3 illustrations in colour
Topics