Large deviations for voter model occupation times in two dimensions

Details Large deviations for voter model occupation times in two dimensions Large deviations for voter model occupation times in two dimensions

2007-01-25

arxiv.org/abs/math/0701754v2

Mathematics

Probability

14 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Large deviations for voter model occupation times in two dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Large deviations for voter model occupation times in two dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations for voter model occupation times in two dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329213