Discrete & Computational Geometry

, Volume 39, Issue 1–3, pp 469–499 | Cite as

An Inscribing Model for Random Polytopes

Article

Abstract

For convex bodies K with \(\mathcal {C}^{2}\) boundary in ℝ d , we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volume of these random polytopes. We provide results concerning the variance and higher moments of this functional, as well as an analogous central limit theorem.

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsUCSDLa JollaUSA
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

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