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.

中文翻译：

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两种粒子和优先级接触过程的亚稳定性

我们考虑 $\mathbb{Z}$ 上的对称有限范围接触过程，具有两种类型的粒子（或感染），它们根据相同的超临界速率传播并以 $1$ 的速率死亡（或治愈）。类型 1 的粒子可以占据 $(-\infty, 0]$ 中空的或被类型 2 粒子占据的任何位置，类似地，类型 2 的粒子可以占据 $[1,+\infty) 中的任何位置$ 是空的或被类型 1 的粒子占据。我们考虑模型限制在有限区间 $[-N + 1,N] \cap \mathbb{Z}$。如果初始配置是 $\mathbf{1}_ {(-N,0]}+2\mathbf{1}_{[1,N)}$，我们证明该系统表现出两种亚稳态：一种具有两个物种，另一个物种与在竞争中幸存下来的家庭。