## Gaussian fluctuations for edge counts in high-dimensional random geometric graphs

Autor(en): | Grygierek, Jens Thaele, Christoph |

Stichwörter: | Central limit theorem; Edge counting statistic; High dimensional random geometric graph; Mathematics; Poisson point process; Second-order Poincare inequality; Statistics & Probability; Stochastic geometry |

Erscheinungsdatum: | 2020 |

Herausgeber: | ELSEVIER |

Journal: | STATISTICS & PROBABILITY LETTERS |

Volumen: | 158 |

Zusammenfassung: | Consider a stationary Poisson point process in R-d and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric graph. The number of edges of this graph is counted that have midpoint in the d-dimensional unit ball. A quantitative central limit theorem for this counting statistic is derived, as the space dimension d and the intensity of the Poisson point process tend to infinity simultaneously. (C) 2019 Elsevier B.V. All rights reserved. |

ISSN: | 01677152 |

DOI: | 10.1016/j.spl.2019.108674 |

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