An Inscribing Model for Random Polytopes

An Inscribing Model for Random Polytopes

For convex bodies K with 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 a...

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Veröffentlicht in:Discrete & computational geometry 2008-03, Vol.39 (1-3), p.469-499
Hauptverfasser: Richardson, Ross M., Vu, Van H., Wu, Lei
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computational Mathematics and Numerical Analysis
Geometry
Mathematics
Mathematics and Statistics
Theorems
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Zusammenfassung:For convex bodies K with 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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-007-9012-3