EXPONENTIAL DECAY FOR SUBCRITICAL CONTACT AND PERCOLATION PROCESSES

被引：72

作者：

BEZUIDENHOUT, C ^{[1
]}

GRIMMETT, G ^{[1
]}

机构：

[1] UNIV BRISTOL,SCH MATH,BRISTOL BS8 1TW,AVON,ENGLAND

来源：

ANNALS OF PROBABILITY | 1991年 / 19卷 / 03期

关键词：

CONTACT PROCESS; PERCOLATION;

D O I：

10.1214/aop/1176990332

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 study the contact process, together with a version of the percolation process with one continuously varying coordinate. It is proved here that the radius of the infected cluster has an exponentially decaying tail throughout the subcritical phase. The same is true of the Lebesgue measure (in space-time) of this cluster. Certain critical-exponent inequalities are derived and the critical point of the percolation process in two dimensions is determined exactly.

引用

页码：984 / 1009

页数：26

共 26 条

[1] SHARPNESS OF THE PHASE-TRANSITION IN PERCOLATION MODELS [J].