  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.
