Barany, I;
(1999)
Sylvester's question: The probability that n points are in convex position.
**ANN PROBAB**
, 27
(4)
2020 - 2034.

## Abstract

For a convex body K in the plane, let p(n, K) denote the probability that n random, independent, and uniform points from K are in convex position, that is, none of them lies in the convex hull of the others. Here we determine the asymptotic behavior of p(n, K) by showing that, as n goes to infinity, n(2) (n)root(p(n, K)) tends to a finite and positive limit.

Type: | Article |
---|---|

Title: | Sylvester's question: The probability that n points are in convex position |

Keywords: | convex sets, affine perimeter, random sample, random points in convex position, limit shape, SETS |

UCL classification: | UCL > School of BEAMS UCL > School of BEAMS > Faculty of Maths and Physical Sciences |

URI: | http://discovery.ucl.ac.uk/id/eprint/154690 |

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