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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