Sylvester's question: The probability that n points are in convex position.
2020 - 2034.
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.
|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
Archive Staff Only