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February 2004 Approximation of smooth convex bodies by random circumscribed polytopes
Károly Böröczky Jr., Matthias Reitzner
Ann. Appl. Probab. 14(1): 239-273 (February 2004). DOI: 10.1214/aoap/1075828053

Abstract

Choose $n$ independent random points on the boundary of a convex body $K \subset \R^d$. The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of $K$ is sufficiently smooth, asymptotic expansions as $n \to \infty$ are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best approximating polytopes.

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Károly Böröczky Jr.. Matthias Reitzner. "Approximation of smooth convex bodies by random circumscribed polytopes." Ann. Appl. Probab. 14 (1) 239 - 273, February 2004. https://doi.org/10.1214/aoap/1075828053

Information

Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1049.60009
MathSciNet: MR2023022
Digital Object Identifier: 10.1214/aoap/1075828053

Subjects:
Primary: 52A22 , 60D05

Keywords: circumscribed polytopes , Convex bodies , random approximation

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 1 • February 2004
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