Probability on graphs : random processes on graphs and lattices / Geoffrey Grimmett.

Format:

Book

Author/Creator:

Grimmett, Geoffrey, author.

Series:

Institute of Mathematical Statistics textbooks ; 1.

Institute of Mathematical Statistics textbooks ; 1

Language:

English

Subjects (All):

Graph theory.

Probabilities.

Physical Description:

1 online resource (xi, 247 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Title; Copyright; Contents; Preface; 1 Random walks on graphs; 2 Uniform spanning tree; 3 Percolation and self-avoiding walk; 4 Association and in.uence; 5 Further percolation; 6 Contact process; 7 Gibbs states; 8 Random-cluster model; 9 Quantum Ising model; 10 Interacting particle systems; 11 Random graphs; 12 Lorentz gas; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-03583-5

1-316-08672-0

1-283-05389-6

9786613053893

0-511-76255-0

1-139-04129-0

1-139-04206-8

1-139-04469-9

1-139-03815-X

1-139-04051-0

OCLC:

710974867