### Abstract

Language | English |
---|---|

Pages | 691-714 |

Number of pages | 24 |

Journal | Advances in Applied Probability |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2004 |

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### Keywords

- spanning tree
- extreme value
- weak convergence
- dickman distribution
- poisson-dirichlet distribution

### Cite this

*Advances in Applied Probability*,

*36*(3), 691-714. https://doi.org/10.1239/aap/1093962229

}

*Advances in Applied Probability*, vol. 36, no. 3, pp. 691-714. https://doi.org/10.1239/aap/1093962229

**Random minimal directed spanning trees and Dickman-type distributions.** / Penrose, M.D.; Wade, Andrew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Random minimal directed spanning trees and Dickman-type distributions

AU - Penrose, M.D.

AU - Wade, Andrew

PY - 2004/9

Y1 - 2004/9

N2 - 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.

AB - 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.

KW - spanning tree

KW - extreme value

KW - weak convergence

KW - dickman distribution

KW - poisson-dirichlet distribution

UR - http://projecteuclid.org/euclid.aap/1093962229

UR - http://www.newton.ac.uk/preprints/NI03088.pdf

U2 - 10.1239/aap/1093962229

DO - 10.1239/aap/1093962229

M3 - Article

VL - 36

SP - 691

EP - 714

JO - Advances in Applied Probability

T2 - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 3

ER -