Probability on Graphs (BOK)

Geoffrey Grimmett

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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-Lowner 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.

Produktfakta

Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2010 Forfatter Geoffrey Grimmett
Forlag
CAMBRIDGE UNIVERSITY PRESS
ISBN 9780521147354
Antall sider 258 Dimensjoner 15,3cm x 22,9cm x 1,4cm
Vekt 390 gram Leverandør Bertram Trading Ltd