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

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

2003-09-10

arxiv.org/abs/math/0309182v2

Annals of Probability 2004, Vol. 32, No. 4, 3301-3323

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000487 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000487

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

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