By Geoffrey Grimmett
This creation to a couple of the crucial versions within the conception of disordered structures leads the reader in the course of the fundamentals, to the very fringe of modern learn, with the minimal of technical fuss. themes lined comprise random stroll, percolation, self-avoiding stroll, interacting particle platforms, uniform spanning tree, random graphs, in addition to the Ising, Potts, and random-cluster types for ferromagnetism, and the Lorentz version for movement in a random medium. Schramm-Löwner evolutions (SLE) come up in a number of contexts. the alternative of subject matters is strongly stimulated via smooth functions and makes a speciality of components that advantage additional learn. particular positive aspects contain an easy account of Smirnov's evidence of Cardy's formulation for severe percolation, and a pretty complete account of the speculation of impression and sharp-thresholds. obtainable to a large viewers of mathematicians and physicists, this publication can be utilized as a graduate direction textual content. each one bankruptcy ends with a number workouts.