Discrete & Computational Geometry

, Volume 6, Issue 3, pp 291–305

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

  • Fernando Affentranger
  • John A. Wieacker
Article

DOI: 10.1007/BF02574691

Cite this article as:
Affentranger, F. & Wieacker, J.A. Discrete Comput Geom (1991) 6: 291. doi:10.1007/BF02574691

Abstract

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.

Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • Fernando Affentranger
    • 1
  • John A. Wieacker
    • 1
  1. 1.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburg i. Br.Germany