The Annals of Probability

Percolation Theory

John C. Wierman

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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


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