Large deviations for voter model occupation times in two dimensions

We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model eta : Z(2) x [0, infinity) -> {0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density rho is an element of (0, 1). In [Probab. Theory Related Fields 77 (1988) 401-413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log(2)(t)].