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November 2003 Existence of quasi-stationary measures for asymmetric attractive particle systems on $\ZZ^d$
Amine Asselah, Fabienne Castell
Ann. Appl. Probab. 13(4): 1569-1590 (November 2003). DOI: 10.1214/aoap/1069786511

Abstract

We show the existence of nontrivial quasi-stationary measures for conservative attractive particle systems on $\ZZ^d$ conditioned on avoiding an increasing local set $\A$. Moreover, we exhibit a sequence of measures $\{\nu_n\}$, whose $\omega$-limit set consists of quasi-stationary measures. For zero-range processes, with stationary measure $\nur$, we prove the existence of an $L^2(\nur)$ nonnegative eigenvector for the generator with Dirichlet boundary on $\A$, after establishing a priori bounds on the $\{\nu_n\}$.

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Amine Asselah. Fabienne Castell. "Existence of quasi-stationary measures for asymmetric attractive particle systems on $\ZZ^d$." Ann. Appl. Probab. 13 (4) 1569 - 1590, November 2003. https://doi.org/10.1214/aoap/1069786511

Information

Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1079.60075
MathSciNet: MR2023889
Digital Object Identifier: 10.1214/aoap/1069786511

Subjects:
Primary: 60J25 , 60K35 , 82C22

Keywords: hitting time , Quasi-stationary measures , Yaglom limit

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 4 • November 2003
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