The Annals of Probability

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

Amine Asselah and Pablo A. Ferrari

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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.

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

First available in Project Euclid: 10 December 2002

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35] 60J25: Continuous-time Markov processes on general state spaces

Quasi-stationary measures exchange processes hitting time Yaglom limit


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.

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