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Boundary domination and the distribution of the largest nearest-neighbor link in higher dimensions

Published online by Cambridge University Press:  14 July 2016

J. Michael Steele  and
Luke Tierney
J. Michael Steele*
Affiliation:
Princeton University
Luke Tierney*
Affiliation:
University of Minnesota
*
∗Postal address: Department of Statistics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA.
∗∗Postal address: School of Statistics, 270 Vincent Hall, 206 Church St SE, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, d ≧ 2, we give limiting distributions for the largest of the nearest-neighbor links. For d ≧ 3 the behavior in the torus is proved to be different from the behavior in the cube. The results given also settle a conjecture of Henze (1982) and throw light on the choice of the cube or torus in some probabilistic models of computational complexity of geometrical algorithms.

Keywords

COMPUTATIONAL GEOMETRYSPIRAL SEARCHEXTREME-VALUE DISTRIBUTIONGUMBEL DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 524 - 528
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported in part by NSF Contract DMS-8414069.

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