Source: Adv. in Appl. Probab.
Volume 36, Number 3
In Bhatt and Roy's minimal directed spanning tree construction for
n random points in the unit square, all edges must be in a
south-westerly direction and there must be a directed path from
each vertex to the root placed at the origin. We identify the
limiting distributions (for large n) for the total length
of rooted edges, and also for the maximal length of all edges in
the tree. These limit distributions have been seen previously in
analysis of the Poisson-Dirichlet distribution and elsewhere; they
are expressed in terms of Dickman's function, and their properties
are discussed in some detail.
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