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Random minimal directed spanning trees and Dickman-type distributions

Penrose, Mathew D.; Wade, Andrew R.

Random minimal directed spanning trees and Dickman-type distributions Thumbnail


Authors

Mathew D. Penrose



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.

Citation

Penrose, M. D., & Wade, A. R. (2004). Random minimal directed spanning trees and Dickman-type distributions. Advances in Applied Probability, 36(3), 691-714. https://doi.org/10.1239/aap/1093962229

Journal Article Type Article
Publication Date Jan 1, 2004
Deposit Date Oct 4, 2012
Publicly Available Date Feb 13, 2013
Journal Advances in Applied Probability
Print ISSN 0001-8678
Electronic ISSN 1475-6064
Publisher Applied Probability Trust
Peer Reviewed Peer Reviewed
Volume 36
Issue 3
Pages 691-714
DOI https://doi.org/10.1239/aap/1093962229
Keywords Spanning tree, Extreme value, Weak convergence, Dickman distribution, Poisson-Dirichlet distribution.

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