By Geoffrey Grimmett
This creation to a couple of the important versions within the concept of disordered structures leads the reader throughout the fundamentals, to the very fringe of modern study, with the minimal of technical fuss. themes lined contain random stroll, percolation, self-avoiding stroll, interacting particle structures, uniform spanning tree, random graphs, in addition to the Ising, Potts, and random-cluster versions for ferromagnetism, and the Lorentz version for movement in a random medium. Schramm-Löwner evolutions (SLE) come up in numerous contexts. the alternative of issues is strongly prompted by means of glossy purposes and specializes in components that advantage extra study. particular beneficial properties contain an easy account of Smirnov's evidence of Cardy's formulation for severe percolation, and a reasonably complete account of the speculation of effect and sharp-thresholds. obtainable to a large viewers of mathematicians and physicists, this e-book can be utilized as a graduate path textual content. every one bankruptcy ends with more than a few routines.