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

2019/07/29 by Machado, Mariela Pentón
#60K35 #82B43 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1907.12662

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.

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