RANDOM-WALK ON THE INFINITE CLUSTER OF THE PERCOLATION MODEL

被引：59
|
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.
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页码：33 / 44
页数：12
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