Indistinguishability of percolation clusters

被引：61

作者：

Lyons, R ^{[1
]}

Schramm, O

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

来源：

ANNALS OF PROBABILITY | 1999年 / 27卷 / 04期

基金：

美国国家科学基金会;

关键词：

finite energy; Cayley graph; group; Kazhdan; wreath product; uniqueness; connectivity; transitive; nonamenable;

D O I：

10.1214/aop/1022874816

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that when percolation produces infinitely many infinite dusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property. This implies that uniqueness of the infinite cluster is equivalent to nondecay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products and inequalities for p(u).

引用

页码：1809 / 1836

页数：28

共 31 条

[1] UNIQUENESS OF THE INFINITE CLUSTER AND CONTINUITY OF CONNECTIVITY FUNCTIONS FOR SHORT AND LONG-RANGE PERCOLATION [J].