Hitting times for special patterns in the symmetric exclusion process on Z^d

Abstract

We consider the symmetric exclusion process {η_t,t>0} on {0,1}^{Z^d}. We fix a pattern A:={η:\sum_Λη(i)\ge k}, where Λis 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 A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for τin a simple way. Also, we characterize the trajectories {η_s,s\le t} conditioned on {τ>t}.