某些乘积图上接触过程的完全收敛定理的证明

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 97-102.

某些乘积图上接触过程的完全收敛定理的证明

姚强

华东师范大学金融与统计学院统计与精算学系上海 200241

收稿日期:2007-12-11 修回日期:2009-01-30 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
国家自然科学基金杰出青年项目(10625101)、重点项目(10531070)和国家重点基础研究发展计划(2006CB805900)资助.

A Proof of the Complete Convergence Theorem for Contact Processes on Some Product Graphs

YAO Qiang

Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University, Shanghai 20024

Received:2007-12-11 Revised:2009-01-30 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金杰出青年项目(10625101)、重点项目(10531070)和国家重点基础研究发展计划(2006CB805900)资助.

摘要/Abstract

摘要：

该文证明了当传染参数充分大时, 乘积图G₁×G₂×Z上的接触过程满足完全收敛定理, 其中G₁和G₂是任意无穷、局部有限的可迁图(从而度有界). 该结果在一定程度上推广了文献[1]的结果.

关键词: 接触过程, 完全收敛定理

Abstract:

In this article a proof of the complete convergence theorem for the basic contact process on the product graph G₁×G₂×Z is given, provided that the infection parameter is large enough, where G₁and G₂ are arbitrary infinite locally finite transitive graphs. It extends the
result of Schonmann [1] in some content.

Key words: Contact process, Complete convergence theorem

中图分类号:

60K35

姚强. 某些乘积图上接触过程的完全收敛定理的证明[J]. 数学物理学报, 2010, 30(1): 97-102.

YAO Qiang. A Proof of the Complete Convergence Theorem for Contact Processes on Some Product Graphs[J]. Acta mathematica scientia,Series A, 2010, 30(1): 97-102.