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 $\{\nu_n\}$.
Citation
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
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