Probability on Graphs: Random Processes on Graphs and Lattices

Grimmett, Geoffrey

ISBN 10: 0521197988 / ISBN 13: 9780521197984

Published by Cambridge Univ Pr, 2010

1st edition. 270 pages. 8.98x6.14x0.79 inches. In Stock. Seller Inventory # zk0521197988

Synopsis:

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm–Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

About the Author: Geoffrey Grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge.

Bibliographic Details

Title: Probability on Graphs: Random Processes on ...
Publisher: Cambridge Univ Pr
Publication Date: 2010
Binding: Hardcover
Condition: Brand New