Random Walk in a Random Environment and First-Passage Percolation on Trees
| dc.creator | Pemantle, Robin | |
| dc.creator | Lyons, Russell | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:02Z | |
| dc.date.available | 2026-07-07T05:07:02Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404045 | |
| dc.identifier | http://arxiv.org/abs/math/0404045 | |
| dc.identifier | Ann. Probab., 20, 125 - 136 (1992) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70702 | |
| dc.subject | Probability | |
| dc.subject | 60J15, 60K35 (Primary) 82A43 (Secondary) | |
| dc.title | Random Walk in a Random Environment and First-Passage Percolation on Trees | |
| dc.type | text |