Annals of Applied Probability

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

Amine Asselah and Fabienne Castell

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

First available in Project Euclid: 25 November 2003

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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 hitting time Yaglom limit


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.

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