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

Understand

Consider a stationary Poisson point process in $\mathbb{R}^d$ 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.