Penrose, M.D. and Wade, Andrew
(2004)
*Random minimal directed spanning trees and Dickman-type distributions.*
Advances in Applied Probability, 36 (3).
pp. 691-714.
ISSN 0001-8678

## 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.

Item type: | Article |
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ID code: | 34462 |

Keywords: | spanning tree, extreme value, weak convergence, dickman distribution, poisson-dirichlet distribution, Probabilities. Mathematical statistics, Applied Mathematics, Statistics and Probability |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 04 Nov 2011 12:53 |

Last modified: | 05 Sep 2014 11:00 |

URI: | http://strathprints.strath.ac.uk/id/eprint/34462 |

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