A STRONG LAW FOR THE LONGEST EDGE OF THE MINIMAL SPANNING TREE
By Mathew D. Penrose.
are independent random points in d-dimensional
space with common density f, having compact
connected support A with smooth boundary.
Suppose the restriction of
f to A is continuous.
be the smallest r such that the union of balls of diameter
r centred at the first n points is connected.
derive an almost sure limit for n
(Mn)d/ log n .
Annals of Probability 27, 290-298 (1999).