A Strong Law for the Largest Nearest-Neighbor Link on Normally Distributed Points
arXiv:math/0604585
Abstract
Let points be placed independently in dimensional space according to the standard dimensional normal distribution. Let be the longest edge length for the nearest neighbor graph on these points. We show that \[\lim_{n \rar \infty} \frac{\sqrt{\log n} d_n}{\log \log n} = \frac{d}{\sqrt{2}}, \qquad d \geq 2, {a.s.} \]
10 pages