Coexistence for Richardson type competing spatial growth models
| dc.creator | Hoffman, Christopher | |
| dc.date | 2004-05-19 | |
| dc.date.accessioned | 2026-07-07T05:08:24Z | |
| dc.date.available | 2026-07-07T05:08:24Z | |
| dc.description | We study a large family of competing spatial growth models. In these the vertices in Z^d can take on three possible states {0,1,2}. Vertices in states 1 and 2 remain in their states forever, while vertices in state 0 which are adjacent to a vertex in state 1 (or state 2) can switch to state 1 (or state 2). We think of the vertices in states 1 and 2 as infected with one of two infections while the vertices in state 0 are considered uninfected. In this way these models are variants of the Richardson model. We start the models with a single vertex in state 1 and a single vertex is in state 2. We show that with positive probability state 1 reaches an infinite number of vertices and state 2 also reaches an infinite number of vertices. This extends results and proves a conjecture of Haggstrom and Pemantle. The key tool is applying the ergodic theorem to stationary first passage percolation. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405377 | |
| dc.identifier | http://arxiv.org/abs/math/0405377 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71247 | |
| dc.subject | Probability | |
| dc.subject | 60J25 92B05 | |
| dc.title | Coexistence for Richardson type competing spatial growth models | |
| dc.type | text |