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中国科学院大学学报 ›› 2014, Vol. 31 ›› Issue (4): 445-452.DOI: 10.7523/j.issn.2095-6134.2014.04.001

• 数学 •    下一篇

无穷大开簇上构型出现次数的强大数律和中心极限定理

唐鹏飞, 郭田德   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2013-05-06 修回日期:2013-07-31 发布日期:2014-07-15
  • 通讯作者: 唐鹏飞,E-mail:tangpengfei11@mails.ucas.ac.cn
  • 基金资助:

    Supported by National Natural Science Foundation of China (71271204,11331012,11101420)

SLLN and CLT for patterns on the infinite open cluster

TANG Pengfei, GUO Tiande   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2013-05-06 Revised:2013-07-31 Published:2014-07-15
  • Supported by:

    Supported by National Natural Science Foundation of China (71271204,11331012,11101420)

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Bn)=[-nn]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.

关键词: 渗流, 构型定理, 鞅, 强大数律, 中心极限定理

Abstract:

In this paper, we consider supercritical Bernoulli bond percolation on the integer lattice Ld with parameter p. We study occurrences of patterns on the infinite open cluster. Let Λn denote 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 Λn are obtained.

Key words: percolation, pattern theorem, martingale, strong law of large numbers, central limit theorem

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