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).
| ISBN: | 9783319025759 |
| Publication date: | 19th December 2013 |
| Author: | Itai Benjamini |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 129 pages |
| Series: | Lecture Notes in Mathematics |
| Genres: |
Geometry Stochastics Engineering: Mechanics of solids Mathematical physics Probability and statistics Combinatorics and graph theory |
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).
Coarse Geometry and Randomness features in the following genres: Geometry, Stochastics, Engineering: Mechanics of solids, Mathematical physics, Probability and statistics, Combinatorics and graph theory
Coarse Geometry and Randomness is available in Paperback
Coarse Geometry and Randomness was written by Itai Benjamini and published by Springer an imprint of Springer International Publishing
Coarse Geometry and Randomness has 129 pages
Yes it is part of Lecture Notes in Mathematics series