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

Abstract

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 ρ\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 ρ. This, in turn, permits us to obtain sharp estimates for P_{\nur}(τ>t), where τis the first time the origin is occupied.