Coexistence in two-type first-passage percolation models
| dc.creator | Garet, Olivier | |
| dc.creator | Marchand, Regine | |
| dc.date | 2003-12-18 | |
| dc.date.accessioned | 2026-07-07T06:31:53Z | |
| dc.date.available | 2026-07-07T06:31:53Z | |
| dc.description | We study the problem of coexistence in a two-type competition model governed by first-passage percolation on $\Zd$ or on the infinite cluster in Bernoulli percolation. Actually, we prove for a large class of ergodic stationary passage times that for distinct points $x,y\in\Zd$, there is a strictly positive probability that $\{z\in\Zd;d(y,z)<d(x,z)\}$ and $\{z\in\Zd;d(y,z)>d(x,z)\}$ are both infinite sets. We also show that there is a strictly positive probability that the graph of time-minimizing path from the origin in first-passage percolation has at least two topological ends. This generalizes results obtained by H{ä}ggstr{ö}m and Pemantle for independent exponential times on the square lattice. | |
| dc.description | submitted 18 dec 2003 | |
| dc.identifier | https://arxiv.org/abs/math/0312369 | |
| dc.identifier | http://arxiv.org/abs/math/0312369 | |
| dc.identifier | Annals of Applied Probability 15, No. 1A (2005) pages 298-330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98742 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B43 | |
| dc.title | Coexistence in two-type first-passage percolation models | |
| dc.type | text |