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

## TL;DR

This paper studies a symmetric two-type contact process on a finite interval, revealing the existence of two metastable states: one with both species and one with the surviving dominant species.

## Contribution

It demonstrates the metastable behavior of a two-type contact process with priorities on a finite interval, highlighting the coexistence and competition dynamics.

## Key findings

- Existence of two metastable states in the model
- Metastability persists over long timescales
- Dominant species can survive competition under certain conditions

## 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 $\mathbf{1}_ {(-N,0]}+2\mathbf{1}_{[1,N)}$, 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.