### Abstract

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, 2^{d/2}d^{-e{open}})→1 and Prob(d, 2^{d/2}d^{(3/4)+e{open}})→0 for every fixed e{open}>0 when d→∞. The question whether E_{n} is a k-neighbourly polytope is also investigated.

Original language | English |
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Pages (from-to) | 231-240 |

Number of pages | 10 |

Journal | Probability Theory and Related Fields |

Volume | 77 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1988 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Bárány, I., & Füredi, Z. (1988). On the shape of the convex hull of random points.

*Probability Theory and Related Fields*,*77*(2), 231-240. https://doi.org/10.1007/BF00334039