THE RANDOM CONNECTION MODEL AND FUNCTIONS OF EDGE-MARKED POISSON PROCESSES: SECOND ORDER PROPERTIES AND NORMAL APPROXIMATION

• 成果类型: Article
• 署名作者: Last, Guenter; Nestmann, Franz; Schulte, Matthias
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; Heriot Watt University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1585
• 发表日期: 2021
• 页码: 128-168
• 关键词: CENTRAL LIMIT-THEOREMS; Random graphs; percolation

摘要

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these component counts as well as a qualitative central limit theorem for the total number of finite components. To this end we first derive general results for functions of edge marked Poisson processes, which we believe to be of independent interest.