A note on estimating the dimension from a random geometric graph

Caelan Atamanchuk, Luc Devroye, Gabor Lugosi

Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\dots ,X_n$ drawn from an unknown density $f$ on ${\mathbb{R}}^d$. An edge $(i,j)$ is pre…