On a conjecture of R. E. Miles about the convex hull of random points (Q1076977)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On a conjecture of R. E. Miles about the convex hull of random points |
scientific article; zbMATH DE number 3955877
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a conjecture of R. E. Miles about the convex hull of random points |
scientific article; zbMATH DE number 3955877 |
Statements
On a conjecture of R. E. Miles about the convex hull of random points (English)
0 references
1986
0 references
Denote by \(p_{d+i}(B_ d,d+m)\) the probability that the convex hull of \(d+m\) points chosen independently and uniformly from a d-dimensional ball \(B_ d\) possesses \(d+i\) \((i=1,...,m)\) vertices. Miles' conjecture that \(p_{d+m}(B_ d,d+m)\to 1\) as \(d\to \infty\) is proved for any integer m. (This is obvious for \(m=1\) and was shown by Kingman for \(m=2\) and by Miles for \(m=3.)\) Further, a related result by Miles is generalized, and several consequences are deduced.
0 references
convex hull of random points
0 references
random polytopes
0 references
0 references
