RANDOM-WALK IN A RANDOM ENVIRONMENT AND 1ST-PASSAGE PERCOLATION ON TREES
成果类型：
Article
署名作者：
LYONS, R; PEMANTLE, R
署名单位：
University of Wisconsin System; University of Wisconsin Madison; Stanford University; University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989920
发表日期：
1992
页码：
125-136
关键词：
摘要：
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches per vertex. This generalizes and unifies previous work of the authors. It also shows that the point of phase transition for edge-reinforced random walk is likewise determined by the branching number of the tree. Finally, we show that the branching number determines the rate of first-passage percolation on trees, also known as the first-birth problem. Our techniques depend on quasi-Bernoulli percolation and large deviation results.