A Strong Law for the Largest Nearest-Neighbor Link on Normally   Distributed Points
  Let $n$ points be placed independently in $d-$dimensional space according to the standard $d-$dimensional normal distribution. Let $d_n$ be the longest edge length for the nearest neighbor graph on these points. We show that \[\lim_{n \rar \infty} \frac{\sqrt{\log n} d_n}{\log \log n} = \frac{d}{\sqrt{2}}, \qquad d \geq 2, {a.s.} \] 
Bhupender Gupta (I.I.T.Kanpur), Srikanth K. Iyer (I.I.Sc.Bangalore)