Probability on Graphs: Random Processes on Graphs and Lattices (Institute of Mathematical Statistics Textbooks, Series Number 1) - Hardcover

Grimmett, Geoffrey

Hardcover

ISBN 10: 0521197988 ISBN 13: 9780521197984

Publisher: Cambridge University Press, 2010

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 this title

Book Description

Grimmett's concise and masterful introduction to the basic mathematical ideas needed to model such random processes as viral marketing, epidemics, random algorithms, and efficient routing. The selection of topics and the approach taken to them is strongly motivated by modern applications. Each chapter ends with exciting exercises.

About the Author

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2010
• ISBN 10: 0521197988
• ISBN 13: 9780521197984
• Binding: Hardcover
• Language: English
• Number of pages: 260