Recurrence and Polya Number of General One-Dimensional Random Walks  

作　　者：张晓琨 万晶 陆静菊 徐新平 

机构地区：[1]School of Physical Science and Technology,Soochow University

出　　处：《Communications in Theoretical Physics》2011年第8期293-296,共4页理论物理通讯（英文版）

基　　金：Supported by National Natural Science Foundation of China under Grant No. 10975057;Doctor Fund Project of Ministry of Education under Contract 20103201120003;the New Teacher Foundation of Soochow University under Contracts Q3108908, Q4108910;the Extracurricular Pesearch Foundation of Undergraduates under Grant No. KY2010056A

摘　　要：The recurrence properties of random walks can be characterized by P61ya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities l and r, or remain at the same position with probability o （l ＋ r ＋ o = 1）. We calculate Polya number P of this model and find a simple expression for P as, P = 1 - △, where △ is the absolute difference of l and r （△= ｜l - r｜）. We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability l equals to the right-moving probability r.

关 键 词：random walk return probability Polya number 

分 类 号：O211.6[理学—概率论与数理统计]