Hitting times for special patterns in the symmetric exclusion process on ℤd

Abstract

We consider the symmetric exclusion process {η_t,t>0} on {0,1}^ℤd. We fix a pattern ${\mathcal{A}}:=\{\eta: \sum_{\Lambda}\eta(i)\ge k\}$, where Λ is a finite subset of ℤ^d and k is an integer, and we consider the problem of establishing sharp estimates for τ, the hitting time of ${\mathcal{A}}$. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for τ in a simple way. Also, we characterize the trajectories {η_s,s≤t} conditioned on {τ>t}.