Open Access
Translator Disclaimer
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


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.


Download Citation

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


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

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

Primary: 52A22 , 60D05

Keywords: circumscribed polytopes , Convex bodies , random approximation

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 1 • February 2004
Back to Top