A FUNCTIONAL CENTRAL LIMIT THEOREM FOR SI PROCESSES ON CONFIGURATION MODEL GRAPHS
A FUNCTIONAL CENTRAL LIMIT THEOREM FOR SI PROCESSES ON CONFIGURATION MODEL GRAPHS
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DOI：
10.1017/apr.2022.52
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发表时间：
2022-09-01
影响因子：
1.2
通讯作者：
Koeppl, Heinz
中科院分区：
文献类型：
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作者：
Khudabukhsh, Wasiur R.;Woroszylo, Casper;Koeppl, Heinz
研究了在有限时间区间上具有给定度分布的配置模型随机图上的随机区室传染病过程。我们将图顶点的种群分成两个隔间，即S和I，分别表示易感和感染的顶点。除了这两个分区的大小，我们还跟踪SI-边（连接易感和感染顶点的边）和SS-边（连接两个易感顶点的边）的计数。我们描述了这些计数的动力学过程，并提出了一个函数的中心极限定理（FCLT）的随机图中的顶点数增长到无穷大。FCLT断言，计数，当适当的缩放，弱收敛到一个连续的高斯向量半鞅过程在空间中的向量值cadlag函数赋予Skorokhod拓扑。本文讨论了FCLT在逾渗理论和计算机病毒传播模型中的应用。我们还提供了模拟结果，说明了一些常见的度分布的FCLT。
We study a stochastic compartmental susceptible-infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a func-tional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued cadlag functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of com-puter viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.