拟顶点可迁图上简单随机游走的切割点  

Cutpoints for Simple Random Walks on Quasi-Transitive Graphs

作　　者：宋贺[1] 向开南 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《数学学报（中文版）》2017年第6期947-954,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11271204;11671216)

摘　　要：证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.We prove that a simple random walk on quasi-transitive graphs with the volume growth being at least as fast as a polynomial of degree 5 has a.s. infinitely many cut times, and hence infinitely many cutpoints. This confirms a conjecture raised by Benjamini, Gurel-Gurevich and Schramm [2011, Cutpoints and resistance of random walk paths, Ann. Probab., 39（3）： 1122-1136] that PATH of a simple random walk on any transient vertex-transitive graph has a.s. infinitely many cutpoints in the corresponding case.

关 键 词：切割点 简单随机游走 暂留 拟顶点可迁图 

分 类 号：O211.62[理学—概率论与数理统计]