, Volume 6, Issue 1, pp 291-305

On the convex hull of uniform random points in a simpled-polytope

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Abstract

Denote the expected number of facets and vertices and the expected volume of the convex hullP n ofn random points, selected independently and uniformly from the interior of a simpled-polytope byE n (f), E n (v), andE n (V), respectively. In this note we determine the sharp constants of the asymptotic expansion ofE n (f), E n (v), andE n (V), asn tends to infinity. Further, some results concerning the expected shape ofP n are given.

Communicated by Rolf Schneider
The work of F. Affentranger was supported by the Swiss National Foundation.