Occupation time large deviations of the voter model

This paper is a sequel to [5] and [6]. We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model ζ_t (see e.g., [11] or [8]). In keeping with our previous results, we show that the large deviations are "classical" in high dimensions (d≧5 for ζ_t) but "fat" in low dimensions (d≦4). Interaction distinguishes the voter model from the independent particle systems of [5] and [6], and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.