Percolation Theory and First-Passage Percolation

Harry Kesten

doi:10.1214/aop/1176991975

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Home > Journals > Ann. Probab. > Volume 15 > Issue 4 > Article

October, 1987 Percolation Theory and First-Passage Percolation

Harry Kesten

Ann. Probab. 15(4): 1231-1271 (October, 1987). DOI: 10.1214/aop/1176991975

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Abstract

We give a survey of some of the principal results in percolation theory and first-passage percolation. No proofs are given. Open problems abound and are usually displayed with a number ($\ast$ P).

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Harry Kesten. "Percolation Theory and First-Passage Percolation." Ann. Probab. 15 (4) 1231 - 1271, October, 1987. https://doi.org/10.1214/aop/1176991975

Information

Published: October, 1987

First available in Project Euclid: 19 April 2007

zbMATH: 0629.60103

MathSciNet: MR905330

Digital Object Identifier: 10.1214/aop/1176991975

Subjects:

Primary: 60K35

Secondary: 60K10 , 82A43 , 82A68

Keywords: asymptotic shape , Critical exponents , Eden's model , First-passage percolation , flow problem , Incipient infinite cluster , Invasion percolation , minimal surfaces , percolation , phase transition , power laws , resistance of random networks , scaling relations , time constants