Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5

Details Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5 Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5

2001-09-24

arxiv.org/abs/math/0109189v2

Ann. Probab. 30 (2002), no. 4, 1913--1932

Mathematics

Probability

18 pages. Corrections after referee report. To be published in Ann Probab

Scientific paper

10.1214/aop/1039548376

We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each \rho\in ]0,1[, we establish uniqueness of the density of quasi-stationary measures in L^2(d\nur), where \nur is the stationary measure of density \rho. This, in turn, permits us to obtain sharp estimates for P_{\nur}(\tau>t), where \tau is the first time the origin is occupied.

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