A short proof of the Harris-Kesten theorem

被引：28

作者：

Bollobas, Bela ^{[1
]}

Riordan, Oliver

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[2] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England

[3] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2006年 / 38卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1112/S002460930601842X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice Z(2) is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at p = 1/2. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any p > 1/2.

引用

页码：470 / 484

页数：15

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