随机游动的常返和相遇问题  

Recurrence and Collisions of Random Walks

作　　者：陈大岳[1] 章复熹[1] 

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学进展》2014年第2期175-182,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金资助课题(No.10271026);973计划(No.2011CB808000)资助

摘　　要：本文综述随机游动的常返和相遇问题的研究历史.首先回顾随机游动的各种定义.对于常返问题,考察其与电阻的联系,探究图上随机游动与其子图上随机游动的关系.关于相遇问题,本文讨论已知结论、应用背景和尚待研究的几个命题.We discuss issues concerning the recurrence and collisions of simple random walks on a graph. After reviewing various definitions of a random walk, we study the connection of random walks with electrical networks. In particular we would like to find out whether a subgraph shares with the graph the same property in term of recurrence of random walk. For collisions of random walks, we present some open problems as well as recent results with possible applications. It is our hope that this review will encourage further studies in this field.

关 键 词：随机游动 常返 相遇 有效电阻 热核估计 

分 类 号：O211.62[理学—概率论与数理统计]