Coarse geometry and randomness : École d'été de probabilitiés de SaintFlour XLI  2011
 Responsibility
 Itai Benjamini.
 Language
 English.
 Publication
 Cham [Switzerland] : Springer, [2013]
 Copyright notice
 ©2013
 Physical description
 vii, 129 pages : ill. ; 23 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2100.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA3 .L28 V.2100  Unknown 
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Creators/Contributors
 Author/Creator
 Itai, Benjamini.
 Contributor
 Ecole d'été de probabilités de SaintFlour (41st : 2011)
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 125129).
 Contents

 Isoperimetry and expansions in graphs. Several metric notions. The hyperbolic plane and hyperbolic graphs. More on the structure of vertex transitive graphs. Percolation on graphs. Local limits of graphs. Random planar geometry. Growth and isoperimetric profile of planar graphs. Critical percolation on nonamenable groups. Uniqueness of the infinite percolation cluster. Percolation perturbations. Percolation on expanders. Harmonic functions on graphs. Nonamenable Liouville graphs.
 (source: Nielsen Book Data)
 Publisher's Summary
 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).
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Lecture notes in mathematics, 00758434 ; 2100
 ISBN
 9783319025759
 3319025759
 9783319025766 (eBook)