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On the shape of the convex hull of random points
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  • Published: February 1988

On the shape of the convex hull of random points

  • Imre Bárány1 &
  • Zoltán Füredi2 

Probability Theory and Related Fields volume 77, pages 231–240 (1988)Cite this article

  • 278 Accesses

  • 18 Citations

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Summary

Denote by E n the convex hull of n points chosen uniformly and independently from the d-dimensional ball. Let Prob(d, n) denote the probability that E n has exactly n vertices. It is proved here that Prob(d, 2d/2 d -ɛ)→1 and Prob(d, 2d/2 d (3/4)+ɛ)→0 for every fixed ɛ>0 when d→∞. The question whether E n is a k-neighbourly polytope is also investigated.

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Author information

Authors and Affiliations

  1. School of OR & IE, Cornell University, 14853, Ithaca, NY, USA

    Imre Bárány

  2. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Zoltán Füredi

Authors
  1. Imre Bárány
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  2. Zoltán Füredi
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Bárány, I., Füredi, Z. On the shape of the convex hull of random points. Probab. Th. Rel. Fields 77, 231–240 (1988). https://doi.org/10.1007/BF00334039

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  • Received: 23 May 1986

  • Revised: 19 October 1987

  • Issue Date: February 1988

  • DOI: https://doi.org/10.1007/BF00334039

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Keywords

  • Hull
  • Stochastic Process
  • Probability Theory
  • Convex Hull
  • Statistical Theory
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