Random Walk in a Random Environment and First-Passage Percolation on Trees
概率论
2007-05-23 v1
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.
引用
@article{arxiv.math/0404045,
title = {Random Walk in a Random Environment and First-Passage Percolation on Trees},
author = {Robin Pemantle and Russell Lyons},
journal= {arXiv preprint arXiv:math/0404045},
year = {2007}
}
备注
11 pages