Percolation

This book, first published in 2006, is an account of percolation theory and its ramifications.

Bela Bollobás (Author), Oliver Riordan (Author)

9780521872324, Cambridge University Press

Hardback, published 21 September 2006

334 pages, 112 b/w illus.
23.5 x 16.1 x 2 cm, 0.66 kg

'This book contains a complete account of most of the important results in the fascinating area of percolation. Elegant and straightforward proofs are given with minimal background in probability or graph theory. It is self-contained, accessible to a wide readership and widely illustrated with numerous examples. It will be of considerable interest for both beginners and advanced searchers alike.' Zentralblatt MATH

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

Preface
1. Basic concepts
2. Probabilistic tools
3. Percolation on Z2 - the Harris-Kesten theorem
4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky
5. Uniqueness of the infinite open cluster and critical probabilities
6. Estimating critical probabilities
7. Conformal invariance - Smirnov's theorem
8. Continuum percolation
Bibliography
Index
List of notation.

Subject Areas: Materials science [TGM], Technology: general issues [TB], Condensed matter physics [liquid state & solid state physics PHFC], Mathematical modelling [PBWH], Calculus & mathematical analysis [PBK]