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The limit distribution of the largest interpoint distance for distributions supported by ad-dimensional ellipsoid and generalizations

Part of: Limit theorems Stochastic processes Distribution theory Geometric probability and stochastic geometry

Published online by Cambridge University Press:  11 January 2017

Michael Schrempp
Michael Schrempp*
Affiliation:
Karlsruhe Institute of Technology
*
* Postal address: Institute of Stochastics, Karlsruhe Institute of Technology, Englerstr. 2, D-76131 Karlsruhe, Germany. Email address: [email protected]
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Abstract

We study the asymptotic behaviour of the maximum interpoint distance of random points in a d-dimensional ellipsoid with a unique major axis. Instead of investigating only a fixed number of n points as n tends to ∞, we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. Our main result covers the case of uniformly distributed points.

Keywords

Maximum interpoint distancegeometric extreme value theoryPoisson processuniform distribution in an ellipsoid

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60F05: Central limit and other weak theorems
Secondary: 60G55: Point processes 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 1256 - 1270
Copyright
Copyright © Applied Probability Trust 2017 

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