论文标题
将单双重性应用于双接触过程
Applying monoid duality to a double contact process
论文作者
论文摘要
在本文中，我们使用二元技术来研究众所周知的接触过程（CP）和鲜为人知的歼灭分支过程。由于后者可以看作是接触过程的取消版本，因此我们将其重新命名为取消联系过程（CCP）。我们感兴趣的过程将包括两个条目，第一个条目是CP，第二个是CCP。我们将此过程称为双接触过程（2CP），并证明它具有（取决于模型参数），最多是一个不变定律，在两个过程中都存在该定律。特别是，我们可以以单调耦合的方式选择模型参数。在这种情况下，上述不变的法律也将具有CCP中的属性，只有在CP中也有一个位置。在途中，我们扩展了在我们的论文“交换性二元性”中发现的马尔可夫过程的二重性，以在无限状态空间上的过程中进行过程，以便它们尤其可以用于相互作用的粒子系统。
In this paper we use duality techniques to study a combination of the well-known contact process (CP) and the somewhat less-known annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we rebrand it as the cancellative contact process (cCP). Our process of interest will consist of two entries, the first being a CP and the second being a cCP. We call this process the double contact process (2CP) and prove that it has (depending on the model parameters) at most one invariant law under which ones are present in both processes. In particular, we can choose the model parameter in such a way that CP and cCP are monotonely coupled. In this case also the above mentioned invariant law will have the property that, under it, ones in the cCP can only be present at sites where there are also ones in the CP. Along the way we extend the dualities for Markov processes discovered in our paper "Commutative monoid duality" to processes on infinite state spaces so that they, in particular, can be used for interacting particle systems.
