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

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

2002-02-28

arxiv.org/abs/math/0202302v1

Mathematics

Probability

19 pages

Scientific paper

We show the existence of non-trivial 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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