Coarse geometry and randomness École d'Été de Probabilitiés de Saint-Flour XLI - 2011 Itai Benjamini

Format:

Book

Author/Creator:

Itai, Benjamini, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2100

Lecture notes in mathematics 1617-9692 2100

Language:

English

Subjects (All):

Stochastic processes.

Geometry.

geometry.

Physical Description:

1 online resource

Place of Publication:

Cham [Switzerland] Springer [2013]

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)

Contents:

Introductory Graph and Metric Notions On the Structure of Vertex Transitive Graphs The Hyperbolic Plane and Hyperbolic Graphs Percolation on Graphs Local Limits of Graphs Random Planar Geometry Growth and Isoperimetric Profile of Planar Graphs Critical Percolation on Non-Amenable Groups Uniqueness of the Infinite Percolation Cluster Percolation Perturbations Percolation on Expanders Harmonic Functions on Graphs Nonamenable Liouville Graphs

Notes:

Includes bibliographical references (pages 125-129)

Online resource; title from PDF title page (SpringerLink, viewed Jan. 23, 2014)

Other Format:

Print version Itai, Benjamini. Coarse geometry and randomness

ISBN:

9783319025766

3319025767

OCLC:

868901281

Access Restriction:

Restricted for use by site license