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

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  • Pentón Machado, Mariela

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.

Suggested Citation

  • Pentón Machado, Mariela, 2020. "Metastability for the contact process with two types of particles and priorities," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2751-2777.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2751-2777
    DOI: 10.1016/j.spa.2019.08.002
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    References listed on IDEAS

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    1. Durrett, Rick & Swindle, Glen, 1991. "Are there bushes in a forest?," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 19-31, February.
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    More about this item

    Keywords

    Contact process; Percolation;

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