Probability Theory and Related Fields

, Volume 133, Issue 4, pp 483–507

Central limit theorems for random polytopes

Article

DOI: 10.1007/s00440-005-0441-8

Cite this article as:
Reitzner, M. Probab. Theory Relat. Fields (2005) 133: 483. doi:10.1007/s00440-005-0441-8

Abstract

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

Key words or phrases

Random polytopesCLTApproximation of convex bodiesDependency graph

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Inst. of Discrete Mathematics and GeometryUniversity of Technology ViennaViennaAustria