%0 Generic %1 maillard2007large %A Maillard, G. %A Mountford, T. %D 2007 %K large_deviations spatial_structure voter_model %T Large deviations for voter model occupation times in two dimensions %U http://arxiv.org/abs/math/0701754 %X We study the decay rate of large deviation probabilities of occupation times, up to time $t$, for the voter model $\eta\colon\Z^2\times0,ınfty)\ra\0,1\$ with simple random walk transition kernel, starting from a Bernoulli product distribution with density $\rhoın(0,1)$. Bramson, Cox and Griffeath (1988) showed that the decay rate order lies in $łog(t),łog^2(t)$. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are $łog^2(t)$ when the deviation from $\rho$ is maximal (i.e., $\eta0$ or 1), and $łog(t)$ in all other situations.

@misc{maillard2007large, abstract = {We study the decay rate of large deviation probabilities of occupation times, up to time $t$, for the voter model $\eta\colon\Z^2\times[0,\infty)\ra\{0,1\}$ with simple random walk transition kernel, starting from a Bernoulli product distribution with density $\rho\in(0,1)$. 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 $\rho$ is maximal (i.e., $\eta\equiv 0$ or 1), and $\log(t)$ in all other situations.}, added-at = {2013-01-31T00:11:59.000+0100}, author = {Maillard, G. and Mountford, T.}, biburl = {https://www.bibsonomy.org/bibtex/25870c72134e0d0f67b7a6faee087dc98/peter.ralph}, interhash = {a7e1660a5d72bfb873b007d0bf01ea82}, intrahash = {5870c72134e0d0f67b7a6faee087dc98}, keywords = {large_deviations spatial_structure voter_model}, note = {arxiv:math/0701754}, timestamp = {2013-01-31T00:11:59.000+0100}, title = {Large deviations for voter model occupation times in two dimensions}, url = {http://arxiv.org/abs/math/0701754}, year = 2007 }