02309nam a22003618a 4500 CR9780511762550 UkCbUP 20180107143412.0 m|||||o||d|||||||| cr|||||||||||| 100506s2010||||enk s ||1 0|eng|d 9780511762550 (ebook) 9780521197984 (hardback) 9780521147354 (paperback) UkCbUP UkCbUP rda QA166 .G75 2010 511.5 22 Grimmett, Geoffrey, author. Probability on Graphs : Random Processes on Graphs and Lattices / [electronic resource] Geoffrey Grimmett. Cambridge : Cambridge University Press, 2010. 1 online resource (260 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier Institute of Mathematical Statistics Textbooks ; no. 1 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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. Graph theory Probabilities Print version: 9780521197984 Institute of Mathematical Statistics Textbooks ; no. 1. http://dx.doi.org/10.1017/CBO9780511762550 Cambridge Books Online 236492 236492