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

  • Michael Schrempp (a1)
Abstract
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.

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* Postal address: Institute of Stochastics, Karlsruhe Institute of Technology, Englerstr. 2, D-76131 Karlsruhe, Germany. Email address: schrempp@kit.edu
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[1] M. J. B. Appel , C. A. Najim and R. P. Russo (2002). Limit laws for the diameter of a random point set. Adv. Appl. Prob. 34, 110.

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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