论文标题
在多维晶格上与两种类型的颗粒进行分支随机步行
Branching Random Walks with Two Types of Particles on Multidimensional Lattices
论文作者
论文摘要
我们考虑在具有两种类型的颗粒和无限数量的初始颗粒的多维晶格上进行连续的时间分支随机行走。主要的结果致力于研究生成函数的研究以及每种类型的单个粒子产生的亚种群矩的限制行为。我们假设粒子类型不仅与分支定律相互不同，例如在多类分支过程中，而且在步行定律中也有所不同。对于每个晶格点和颗粒的复发随机步行的关键分支过程，研究了颗粒上极限空间聚类在晶格上的影响。还考虑了说明流行传播的模型。在此模型中，我们考虑了两种类型的粒子：产生的感染和免疫力。最初，有一个感染的粒子可以感染其他粒子。在这里，对于晶格点每种类型的粒子的局部数量，我们研究了矩及其限制行为。另外，研究了受感染颗粒的间歇性在每个晶格点进行超临界分支过程。提出了模拟以证明极限学模型的极限聚类的影响。
We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting behavior of the moments of subpopulations generated by a single particle of each type. We assume that particle types differ from each other not only by the laws of branching, as in multi-type branching processes, but also by the laws of walking. For a critical branching process at each lattice point and recurrent random walk of particles, the effect of limit spatial clustering of particles over the lattice is studied. A model illustrating epidemic propagation is also considered. In this model, we consider two types of particles: infected and immunity generated. Initially, there is an infected particle that can infect others. Here, for the local number of particles of each type at a lattice point, we study the moments and their limiting behavior. Additionally, the effect of intermittency of the infected particles is studied for a supercritical branching process at each lattice point. Simulations are presented to demonstrate the effect of limit clustering for the epidemiological model.
