Localization for Branching Random Walks in Random Environment
| dc.creator | Hu, Yueyun | |
| dc.creator | Yoshida, Nobuo | |
| dc.date | 2007-12-05 | |
| dc.date.accessioned | 2026-07-07T08:47:24Z | |
| dc.date.available | 2026-07-07T08:47:24Z | |
| dc.description | We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total population grows as fast as its expectation with strictly positive probability. If,on the other hand, $d \le 2$, or the environment is ``random enough", then the total population grows strictly slower than its expectation almost surely. We show the equivalence between the slow population growth and a natural localization property in terms of "replica overlap". We also prove a certain stronger localization property, whenever the total population grows strictly slower than its expectation almost surely. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0712.0649 | |
| dc.identifier | http://arxiv.org/abs/0712.0649 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143587 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K37 (Primary); 60F05, 60J80, 60K35, 82D30 (Secondary) | |
| dc.title | Localization for Branching Random Walks in Random Environment | |
| dc.type | text |