摘要
考虑定义在整点格网Ld上的参数为p的上临界Bernoulli渗流,研究无穷大开簇上构型的发生情况.用Λn表示一个给定的构型P在限制于框B(n)=[-n,n]d中的无穷大开簇上发生的次数,得到了关于Λn的强大数律和中心极限定理.
In this paper,we consider supercritical Bernoulli bond percolation on the integer lattice Ldwith parameter p. We study occurrences of patterns on the infinite open cluster. Let Λndenote the number of occurrences of a given pattern P on the infinite open cluster restricted in the box B（ n） =[- n,n]d. Strong law of large numbers and central limit theorem for Λnare obtained.
出处
《中国科学院大学学报（中英文）》
CAS
CSCD
北大核心
2014年第4期445-452,483,共9页
Journal of University of Chinese Academy of Sciences
基金
Supported by National Natural Science Foundation of China(71271204,11331012,11101420)
关键词
渗流
构型定理
鞅
强大数律
中心极限定理
percolation
pattern theorem
martingale
strong law of large numbers
central limit theorem
