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

2002/02/28 by A. Asselah, Asselah, A., F. Castell +1
Mathematics · #60J25 #60K35 #82C22 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J25 #msc:60K35 #msc:82C22

paper · pdf · doi:10.48550/arxiv.math/0202302

19 pages

arxiv created 2002/02/28 · arxiv updated 2009/11/30

Abstract

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 \ν_n\, whose ω-limit set consists of quasi-stationary measures. For zero range processes, with stationary measure \nur, we prove the existence of an L²(\nur) nonnegative eigenvector for the generator with Dirichlet boundary on \A, after establishing a priori bounds on the \ν_n\.

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