The random connection model and functions of edge-marked poisson processes: Second order properties and normal approximation

Günter Last, Franz Nestmann, Matthias Schulte

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)128-168
Number of pages41
JournalAnnals of Applied Probability
Volume31
Issue number1
DOIs
Publication statusPublished - 1 Feb 2021

Keywords

  • Central limit theorem
  • Component count
  • Covariance structure
  • Edge marking
  • Gilbert graph
  • Poisson process
  • Random connection model
  • Random geometric graph

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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