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The random connection model and functions of edge-marked poisson processes: Second order properties and normal approximation
Publikationstyp
Journal Article
Date Issued
2021-02
Sprache
English
Author(s)
Volume
31
Issue
1
Start Page
128
End Page
168
Citation
Annals of Applied Probability 31 (1): 128-168 (2021-02)
Publisher DOI
Scopus ID
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.
Subjects
Central limit theorem
Component count
Covariance structure
Edge marking
Gilbert graph
Poisson process
Random connection model
Random geometric graph