幺半群对偶在双接触过程中的应用
Applying monoid duality to a double contact process
摘要：
在本文中，我们使用对偶技术来研究著名的接触过程（CP）和鲜为人知的零化分支过程的组合。由于后者可以被视为接触过程的取消版本，我们将其重新命名为取消接触过程（cCP）。我们感兴趣的流程将由两个条目组成，第一个是CP，第二个是cCP。我们称这个过程的双重接触过程（2CP），并证明它有（取决于模型参数）在最多一个不变的法律下，目前在两个过程。特别地，我们可以选择模型参数，使得CP和cCP单调耦合。在这种情况下，上述不变定律也将具有这样的性质，即在它之下，cCP中的1只能存在于CP中也存在1的位点处。一路上，我们扩展的对偶马尔可夫过程中发现我们的论文“交换幺半群对偶”无限状态空间的过程，使他们，特别是可以用于相互作用的粒子系统。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
