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

Abstract

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.