On a Lower Bound for the Time Constant of First-Passage Percolation
| dc.creator | Wu, Xian-Yuan | |
| dc.creator | Feng, Ping | |
| dc.date | 2008-07-05 | |
| dc.date | 2008-07-13 | |
| dc.date.accessioned | 2026-07-07T09:49:43Z | |
| dc.date.available | 2026-07-07T09:49:43Z | |
| dc.description | We consider the Bernoulli first-passage percolation on $\mathbb Z^d (d\ge 2)$. That is, the edge passage time is taken independently to be 1 with probability $1-p$ and 0 otherwise. Let ${μ(p)}$ be the time constant. We prove in this paper that \[ μ(p_1)-μ({p_2})\ge \frac{μ(p_2)}{1-p_2}(p_2-p_1)\] for all $ 0\leq p_1<p_2< 1$ by using Russo's formula. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0807.0839 | |
| dc.identifier | http://arxiv.org/abs/0807.0839 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164694 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35; 82B43 | |
| dc.title | On a Lower Bound for the Time Constant of First-Passage Percolation | |
| dc.type | text |