Barany, I (1999) Sylvester's question: The probability that n points are in convex position. ANN PROBAB , 27 (4) 2020 - 2034.
Full text not available from this repository.
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 > Faculty of Maths and Physical Sciences > Mathematics |
Archive Staff Only: edit this record