Rooted edges of a minimal directed spanning tree on random points

Abstract

For n independent, identically distributed uniform points in [0, 1] d , d ≥ 2, let L n be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of L n , and show that L n satisfies a central limit theorem, unlike in the case d = 2.

Locations

• Advances in Applied Probability - View - PDF