RANDOM-WALK ON THE INFINITE CLUSTER OF THE PERCOLATION MODEL

被引：60

作者：

GRIMMETT, GR

KESTEN, H

ZHANG, Y

机构：

[1] CORNELL UNIV,DEPT MATH,ITHACA,NY 14853

[2] UNIV COLORADO,DEPT MATH,BOULDER,CO 80309

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1993年 / 96卷 / 01期

关键词：

Mathematics Subject Classification (1991): 60J15; 60K35; 82B43; 82D30;

D O I：

10.1007/BF01195881

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 consider random walk on the infinite cluster of bond percolation on Z(d). We show that, in the supercritical regime when d greater-than-or-equal-to 3, this random walk is a.s. transient. This conclusion is achieved by considering the infinite percolation cluster as a random electrical network in which each open edge has unit resistance. It is proved that the effective resistance of this network between a nominated point and the points at infinity is almost surely finite.

引用

页码：33 / 44

页数：12

共 12 条

[1] AN INVARIANCE-PRINCIPLE FOR REVERSIBLE MARKOV-PROCESSES - APPLICATIONS TO RANDOM MOTIONS IN RANDOM-ENVIRONMENTS [J].