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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Random points on the boundary of smooth convex bodies
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by Matthias Reitzner PDF
Trans. Amer. Math. Soc. 354 (2002), 2243-2278 Request permission

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
  • MR Author ID: 339588
  • Email: Matthias.Reitzner+e1142@tuwien.ac.at
  • 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)
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1885651