## The Annals of Probability

### Regularity of quasi-stationary measures for simple exlusion in dimension d≥5

#### Abstract

We consider the symmetric simple exclusion process on $\ZZ^d$, for $d\geq 5$, and study the regularity of the quasi-stationary measures of the dynamics conditioned 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.

#### Article information

Source
Ann. Probab., Volume 30, Number 4 (2002), 1913-1932.

Dates
First available in Project Euclid: 10 December 2002

https://projecteuclid.org/euclid.aop/1039548376

Digital Object Identifier
doi:10.1214/aop/1039548376

Mathematical Reviews number (MathSciNet)
MR1944010

Zentralblatt MATH identifier
1014.60089

#### Citation

Asselah, Amine; Ferrari, Pablo A. Regularity of quasi-stationary measures for simple exlusion in dimension d ≥5. Ann. Probab. 30 (2002), no. 4, 1913--1932. doi:10.1214/aop/1039548376. https://projecteuclid.org/euclid.aop/1039548376

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