Subcritical contact process seen from the edge: convergence to quasi-equilibrium

The subcritical contact process seen from the rightmost infected site has no invariant measures. We prove that nevertheless it converges in distribution to a quasi-stationary measure supported on finite configurations.

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Bibliographic Details
Published inElectronic journal of probability Vol. 20; no. none; pp. 1 - 16
Main Authors Andjel, Enrique, Ezanno, François, Groisman, Pablo, Rolla, Leonardo
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics (IMS) 2015
Subjects
Mathematics
Probability
2 dimensions
oriented percolation
statistical mechanics models
percolation theory
interacting random processes
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Summary:The subcritical contact process seen from the rightmost infected site has no invariant measures. We prove that nevertheless it converges in distribution to a quasi-stationary measure supported on finite configurations.
ISSN:1083-6489
1083-6489
DOI:10.1214/EJP.v20-3881