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Grimmett's concise and masterful introduction to the basic mathematical ideas needed to model such random processes as viral marketing, epidemics, random algorithms, and efficient routing. The selecti

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most acce

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.

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. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. 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.

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random proces

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most acce

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random proces

Grimmett, Geoffrey: Percolation and disordered systems.- Kesten, Harry: Aspects of first passage percolation.?