Fluctuations of the connectivity threshold and largest nearest-neighbour link

Mathew D. Penrose, Xiaochuan Yang

Consider a random uniform sample of $n$ points in a compact region $A$ of Euclidean $d$-space, $d\ge 2$, with a smooth or (when $d=2$) polygonal boundary. Fix $k\in \mathbf{N}$. Le…