On the shape of the convex hull of random points

Imre Bárány, Zoltán Füredi

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)231-240
Number of pages10
JournalProbability Theory and Related Fields
Volume77
Issue number2
DOIs
Publication statusPublished - Feb 1988

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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