## Annals of Applied Probability

### Existence of quasi-stationary measures for asymmetric attractive particle systems on $\ZZ^d$

#### 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 $\{\nu_n\}$.

#### Article information

Source
Ann. Appl. Probab., Volume 13, Number 4 (2003), 1569-1590.

Dates
First available in Project Euclid: 25 November 2003

https://projecteuclid.org/euclid.aoap/1069786511

Digital Object Identifier
doi:10.1214/aoap/1069786511

Mathematical Reviews number (MathSciNet)
MR2023889

Zentralblatt MATH identifier
1079.60075

#### Citation

Asselah, Amine; Castell, Fabienne. Existence of quasi-stationary measures for asymmetric attractive particle systems on $\ZZ^d$. Ann. Appl. Probab. 13 (2003), no. 4, 1569--1590. doi:10.1214/aoap/1069786511. https://projecteuclid.org/euclid.aoap/1069786511

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