, Volume 77, Issue 3, pp 401-413

Occupation time large deviations of the voter model

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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 ζt (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 ζt) 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.

Dedicated to Frank Spitzer on his 60th birthday
Partially supported by the National Science Foundation under Grant DMS-831080
Partially supported by the National Science Foundation under Grant DMS-841317
Partially supported by the National Science Foundation under Grant DMS-830549