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Few points to generate a random polytope

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Imre Bárány  and
Leoni Dalla
Imre Bárány
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary
Leoni Dalla
Affiliation:
Mathematics Department, Athens University, Athens, 157-81, Greece.
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Abstract

A random polytope, Kn, is the convex hull of n points chosen randomly, independently, and uniformly from a convex body It is shown here that, with high probability, Kn can be obtained by taking the convex hull of m = o(n) points chosen independently and uniformly from a small neighbourhood of the boundary of K.

MSC classification

Secondary: 52A22: Random convex sets and integral geometry
Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 325 - 331
Copyright
Copyright © University College London 1997

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