Existence of quasi-stationary measures for asymmetric attractive particle systems on ᵈ

الأصل · EN

We show the existence of non-trivial quasi-stationary measures for conservative attractive particle systems on ᵈ conditioned on avoiding an increasing local set. Moreover, we exhibit a sequence of measures {νₙ}, whose ω-limit set consists of quasi-stationary measures. For zero range processes, with stationary measure, we prove the existence of an L²() nonnegative eigenvector for the generator with Dirichlet boundary on, after establishing a priori bounds on the {νₙ}.