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


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)→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.


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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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