Large deviations for voter model occupation times in two dimensions
| dc.creator | Maillard, G. | |
| dc.creator | Mountford, T. | |
| dc.date | 2007-01-25 | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:26Z | |
| dc.date.available | 2026-07-07T09:43:26Z | |
| dc.description | We study the decay rate of large deviation probabilities of occupation times, up to time $t$, for the voter model $η\colon\Z^2\times[0,\infty)\ra\{0,1\}$ with simple random walk transition kernel, starting from a Bernoulli product distribution with density $ρ\in(0,1)$. Bramson, Cox and Griffeath (1988) showed that the decay rate order lies in $[\log(t),\log^2(t)]$. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are $\log^2(t)$ when the deviation from $ρ$ is maximal (i.e., $η\equiv 0$ or 1), and $\log(t)$ in all other situations. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701754 | |
| dc.identifier | http://arxiv.org/abs/math/0701754 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162556 | |
| dc.subject | Probability | |
| dc.subject | 60F10; 60K35 | |
| dc.title | Large deviations for voter model occupation times in two dimensions | |
| dc.type | text |