Open Access
August, 1982 Percolation Theory
John C. Wierman
Ann. Probab. 10(3): 509-524 (August, 1982). DOI: 10.1214/aop/1176993764


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.


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John C. Wierman. "Percolation Theory." Ann. Probab. 10 (3) 509 - 524, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0485.60100
MathSciNet: MR659525
Digital Object Identifier: 10.1214/aop/1176993764

Primary: 60K35

Keywords: critical probability , First passage time , percolation , subadditive process

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
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