## The Annals of Probability

- Ann. Probab.
- Volume 10, Number 3 (1982), 509-524.

### Percolation Theory

#### Abstract

An introduction is provided to the mathematical tools and problems of percolation theory. A discussion of Bernoulli percolation models shows the role of graph duality and correlation inequalities in the recent determination of the critical probability in the square, triangular, and hexagonal lattice bond models. An introduction to first passage percolation concentrates on the problems of existence of optimal routes, length of optimal routes, and conditions for convergence of first passage time and reach processes.

#### Article information

**Source**

Ann. Probab., Volume 10, Number 3 (1982), 509-524.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993764

**Digital Object Identifier**

doi:10.1214/aop/1176993764

**Mathematical Reviews number (MathSciNet)**

MR659525

**Zentralblatt MATH identifier**

0485.60100

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Percolation critical probability first passage time subadditive process

#### Citation

Wierman, John C. Percolation Theory. Ann. Probab. 10 (1982), no. 3, 509--524. doi:10.1214/aop/1176993764. https://projecteuclid.org/euclid.aop/1176993764