Abstract
We consider the symmetric exclusion process {ηt,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 ℤd 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 {ηs,s≤t} conditioned on {τ>t}.
Citation
Amine Asselah. Paolo Dai Pra. "Hitting times for special patterns in the symmetric exclusion process on ℤd." Ann. Probab. 32 (4) 3301 - 3323, October 2004. https://doi.org/10.1214/009117904000000487
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