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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Random points on the boundary of smooth convex bodies


Author: Matthias Reitzner
Journal: Trans. Amer. Math. Soc. 354 (2002), 2243-2278
MSC (2000): Primary 60D05, 52A22
DOI: https://doi.org/10.1090/S0002-9947-02-02962-8
Published electronically: February 7, 2002
MathSciNet review: 1885651
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Abstract: The convex hull of $n$ independent random points chosen on the boundary of a convex body $K \subset \mathbb{R}^d$ according to a given density function is a random polytope. The expectation of its $i$-th intrinsic volume for $i=1, \dots, d$ is investigated. In the case that the boundary of $K$ is sufficiently smooth, asymptotic expansions for these expected intrinsic volumes as $n \to \infty$ are derived.


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Additional Information

Matthias Reitzner
Affiliation: Institut für Analysis und Technische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8 – 10, A-1040 Vienna, Austria
Address at time of publication: Institut für Mathematk, Universität Freiburg, Eckerstrasse 1, D-79104 Freiburg, Germany
Email: Matthias.Reitzner+e1142@tuwien.ac.at

DOI: https://doi.org/10.1090/S0002-9947-02-02962-8
Received by editor(s): January 19, 2001
Received by editor(s) in revised form: August 16, 2001
Published electronically: February 7, 2002
Additional Notes: Research supported, in part, by the Austrian Science Foundation (Project J1940-MAT)
Article copyright: © Copyright 2002 American Mathematical Society