乘积图Z^2×{0,1,...,l-1}的常返性的初等证明  

An Elementary Proof for the Recurrence of the Product Graph Z^2 ×{0,1,...,l-1}

作　　者：朱琳 姚强 ZHU Lin;YAO Qiang(Institute of Statistics and Big Data,Renmin University of China,Beijing,100872,China;School of Statistics,East China Normal University,Shanghai,200241,China)

机构地区：[1]中国人民大学统计与大数据研究院,北京100872 [2]华东师范大学统计学院,上海200241

出　　处：《应用概率统计》2018年第3期275-283,共9页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11126236、11201150、11671145)、上海市自然科学基金项目(16ZR1409700)和111引智计划(批准号:B14019)部分资助。

摘　　要：我们已知二维整数格点Z^2是常返的,而三维整数格点Z^3是非常返的.本文严格证明了二维整数格点Z^2与有限线段{0,1,…1,l-1}的乘积图是常返的.证明过程只用到了概率论中的初等方法而没有用到电网络的术语.It is well known that the two dimensional integer lattice Z^2 is recurrent,while the three dimensional integer lattice is transient.In this paper we show that the product graph Z^2×{0,1,...,ι-1}is recurrent.The proof approach only utilizes the elementary methods in probability theory(without the words of electric networks).

关 键 词：随机游动 乘积图 常返性 

分 类 号：O211.62[理学—概率论与数理统计]