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

Jens Grygierek and Christoph Thäle

Statistics & Probability Letters, 2020, vol. 158, issue C

Abstract: Consider a stationary Poisson point process in Rd 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.

Keywords: Central limit theorem; Edge counting statistic; High dimensional random geometric graph; Poisson point process; Second-order Poincaré inequality; Stochastic geometry (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2019.108674

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