On Frieze's \(\zeta\) (3) limit for lengths of minimal spanning trees (Q1090335)

The length of the minimal spanning tree on the complete graph on n vertices with edge weights determined by independent non-negative random variables with distribution F is proved to converge in probability to \(\zeta\) (3)/F'(0), provided only that F have a nonzero derivative at the origin. In particular, no other smoothness or moment conditions are placed on F. This augments the result of Frieze for random variables with finite variances and differentiable distribution.