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

Abstract

We consider a symmetric finite-range contact process on $\mathbb{Z}$ 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 $(-\infty ,0]$ that is empty or occupied by a particle of type 2 and, analogously, particles of type 2 can occupy any site in $[1,+\infty )$ that is empty or occupied by a particle of type 1. We consider the model restricted to a finite interval $[-N+1,N]\cap \mathbb{Z}$. 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.