Asymptotics for Euclidean minimal spanning trees on random points

Abstract

Asymptotic results for the Euclidean minimal spanning tree onn random vertices inRd can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allRd. In particular we prove a conjecture of Robert Bland: the sum of thed'th powers of the edge-lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofRd tends to a constant asn→∞.