Publisher DOI: 10.1214/20-AAP1585
Title: The random connection model and functions of edge-marked poisson processes: Second order properties and normal approximation
Language: English
Authors: Last, Günter 
Nestmann, Franz 
Schulte, Matthias 
Keywords: Central limit theorem; Component count; Covariance structure; Edge marking; Gilbert graph; Poisson process; Random connection model; Random geometric graph
Issue Date: Feb-2021
Source: Annals of Applied Probability 31 (1): 128-168 (2021-02)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/11811
ISSN: 1050-5164
Journal: The annals of applied probability 
Document Type: Article
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