Probability Theory and Related Fields

, Volume 77, Issue 2, pp 231–240 | Cite as

On the shape of the convex hull of random points

  • Imre Bárány
  • Zoltán Füredi
Article
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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/2d-ɛ)→1 and Prob(d, 2d/2d(3/4)+ɛ)→0 for every fixed ɛ>0 when d→∞. The question whether E n is a k-neighbourly polytope is also investigated.

Keywords

Hull Stochastic Process Probability Theory Convex Hull Statistical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Imre Bárány
    • 1
  • Zoltán Füredi
    • 2
  1. 1.School of OR & IECornell UniversityIthacaUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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