Discrete & Computational Geometry

, Volume 1, Issue 4, pp 315–319

Random polytopes in thed-dimensional cube

  • Z. Füredi
Article

Abstract

LetCd be the set of vertices of ad-dimensional cube,Cd={(x1, ...,xd):xi=±1}. Let us choose a randomn-element subsetA(n) ofCd. Here we prove that Prob (the origin belongs to the convA(2d+x→2d))=φ(x)+o(1) ifx is fixed andd → ∞. That is, for an arbitraryε>0 the convex hull of more than (2+ε)d vertices almost always contains 0 while the convex hull of less than (2-ε)d points almost always avoids it.

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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Z. Füredi
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  2. 2.Department of MathematicsM.I.T.CambridgeUSA

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