By Geoffrey Grimmett

This advent to a few of the vital versions within the conception of disordered platforms leads the reader throughout the fundamentals, to the very fringe of modern examine, 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 versions for ferromagnetism, and the Lorentz version for movement in a random medium. Schramm-Löwner evolutions (SLE) come up in a variety of contexts. the alternative of themes is strongly encouraged via sleek functions and specializes in components that benefit extra examine. distinctive positive aspects comprise an easy account of Smirnov's evidence of Cardy's formulation for severe percolation, and a reasonably complete account of the idea 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. every one bankruptcy ends with various workouts.

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