CUTPOINTS AND RESISTANCE OF RANDOM WALK PATHS
成果类型：
Article
署名作者：
Benjamini, Itai; Gurel-Gurevich, Ori; Schramm, Oded
署名单位：
Weizmann Institute of Science; Microsoft
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/10-AOP569
发表日期：
2011
页码：
1122-1136
关键词：
摘要：
We construct a bounded degree graph G, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also prove that the expected number of cutpoints of any transient Markov chain is infinite. This answers two questions of James, Lyons and Peres [A Transient Markov Chain With Finitely Many Cutpoints (2007) Festschrift for David Freedman]. Additionally, we consider a simple random walk on a finite connected graph G that starts at some fixed vertex x and is stopped when it first visits some other fixed vertex y. We provide a lower bound on the expected effective resistance between x and y in the path of the walk, giving a partial answer to a question raised in [Ann. Probab. 35 (2007) 732-738].