Metastability for the contact process with two types of particles and priorities

Mariela Pentón Machado

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2751-2777

Abstract: We consider a symmetric finite-range contact process on Z with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate 1. Particles of type 1 can occupy any site in (−∞,0] that is empty or occupied by a particle of type 2 and, analogously, particles of type 2 can occupy any site in [1,+∞) that is empty or occupied by a particle of type 1. We consider the model restricted to a finite interval [−N+1,N]∩Z. If the initial configuration is 1(−N,0]+21[1,N), we prove that this system exhibits two metastable states: one with the two species and the other one with the family that survives the competition.

Keywords: Contact process; Percolation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:5:p:2751-2777

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DOI: 10.1016/j.spa.2019.08.002

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