by Geoffrey Grimmett

Grundlehren der mathematischen Wissenschaften, vol 321, Springer, 1999.

- Reorganization and expansion of certain material.
- Inclusion of
much fundamental new material such as:
- some material on site percolation, and inhomogeneous percolation,
- strict inequalities between critical points, enhancements etc,
- the relationship between percolation in slabs and in the whole space,
- dynamic and static renormalization,
- Burton-Keane proof of the uniqueness of the infinite cluster,
- sketch of the the lace expansion and mean field theory,
- short essays on further applications, including entanglement and rigidity in percolation, random-cluster model, contact model, stochastic pin-ball, etc.

The first edition had 296 pages, and the second has 444 pages in about the same format. Links to two sample chapters are given below.

* The copyright of all linked material
rests with either the author or with Springer.*

Chapter 1: What is Percolation? This introductory chapter (in pdf format) has been augmented by a new section on site percolation.

Chapter 3: Critical Probabilities A new chapter (in pdf format) discussing critical probabilities, strict inequalities between them, enhancements, and the like.