论文标题
一维接触过程与两种类型的粒子和优先级的收敛性
Convergence of the one-dimensional contact process with two types of particles and priority
论文作者
论文摘要
我们考虑在$ \ mathbb {z} $上使用两种类型的粒子（或感染）上的对称有限范围接触过程，该粒子（或感染）根据相同的超临界率和死亡率（或治愈）以$ 1 $ $ 1 $进行传播。 $ 1 $的类型粒子可以输入$（ - \ infty，0] $的任何站点，该网站被$ 2 $的粒子占用或占用，类似于$ 2 $的粒子可以输入任何$ [1，\ infty）$的粒子，该网站是空的或由$ 1 $的类型粒子占用的。而且，几乎一个粒子可以占据每个位置。我们证明，从$（ - \ infty，0] $中的所有站点开始的过程，由类型1的粒子和$ [1，\ infty）$占用的所有站点占据了2型粒子在分布中收集到与经典接触过程的非平凡不变量度不同的不变量度。此外，我们证明，对于任何初始配置，过程将收敛到四个不变度度量的凸组合。
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 enter any site in $(-\infty,0]$ that is empty or occupied by a particle of type $2$ and, analogously, particles of type $2$ can enter any site in $[1,\infty)$ that is empty or occupied by a particle of type $1$. Also, almost one particle can occupy each site. We prove that the process beginning with all sites in $(-\infty,0]$ occupied by particles of type 1 and all sites in $[1,\infty)$ occupied by particles of type 2 converges in distribution to an invariant measure different from the nontrivial invariant measure of the classic contact process. In addition, we prove that for any initial configuration the process converges to a convex combination of four invariant measures.
