Random minimal directed spanning trees and Dickman-type distributions
Mathew D. Penrose and Andrew R. Wade
Source: Adv. in Appl. Probab. Volume 36, Number 3
(2004), 691-714.
Abstract
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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Keywords: Spanning tree; extreme value; weak convergence; Dickman distribution; Poisson-Dirichlet distribution
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1093962229
Digital Object Identifier: doi:10.1239/aap/1093962229
Mathematical Reviews number (MathSciNet): MR2079909
Zentralblatt MATH identifier: 02149722
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