On the convex hull of uniform random points in a simpled-polytope
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- Affentranger, F. & Wieacker, J.A. Discrete Comput Geom (1991) 6: 291. doi:10.1007/BF02574691
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Denote the expected number of facets and vertices and the expected volume of the convex hullPn ofn random points, selected independently and uniformly from the interior of a simpled-polytope byEn(f), En(v), andEn(V), respectively. In this note we determine the sharp constants of the asymptotic expansion ofEn(f), En(v), andEn(V), asn tends to infinity. Further, some results concerning the expected shape ofPn are given.