Duals and thinnings of some relatives of the contact process

泊松过程的邻域计数依赖稀疏：相关结构与泊松近似

Neighbour-count dependent thinning of Poisson processes: correlation structure and Poisson approximation

本文研究邻域计数依赖的泊松过程局部稀疏算子$T_r$，推导其精确强度、成对相关函数与点模式调控机制，通过三种路径给出有界窗口上的泊松近似误差界。

Applying monoid duality to a double contact process

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…

New Results for the Two-Stage Contact Process

Here we continue the work started by Steve Krone on the two-stage contact process. We give a simplified proof of the duality relation, and answer most of the open questions posed in that paper. We also fill in the details of an incomplete proof.

Duality and Complete Convergence for Multi-type Additive Growth Models

We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional characterizations of these systems, in spacetime as percolation models, and biologically as population models in which the interactions are due to crowding. We prove a necessary and sufficient condition for the model to preserve positive correlations. We then show that complete convergence on $\mathbb{Z}^d$ holds for a large subclass of models including the two-stage con…

若干流行病传播模型的对偶性

Duality for some models of epidemic spreading

本文针对三种一维流行病传播模型建立对偶关系，揭示开放边界下DCP与GDCP自对偶性破坏且遍历但非吸收，而对偶过程吸收但非遍历，并给出稳态关联函数及SIR模型非局域对偶的显式表达。