Limit theorems for random polytopes with vertices on convex surfaces

  • We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen independently and uniformly at random on the boundary of a smooth convex body in \(\mathbb{R}^{d}\). We present both lower and upper variance bounds, a strong law of large numbers, and a central limit theorem for the intrinsic volumes of \(\it K_{n}\). A normal approximation bound from Stein's method and estimates for surface bodies are among the tools involved.

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Metadaten
Author:Nicola TurchiGND, Florian WespiGND
URN:urn:nbn:de:hbz:294-69091
DOI:https://doi.org/10.1017/apr.2018.58
Parent Title (English):Advances in applied probability
Publisher:Cambridge University Press
Place of publication:Cambridge
Document Type:Article
Language:English
Date of Publication (online):2020/01/23
Date of first Publication:2018/11/29
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:Central limit theorem; intrinsic volume; random polytope; stochastic geometry; surface body; variance
Volume:50
Issue:4
First Page:1227
Last Page:1245
Note:
© Copyright Cambridge University Press. Permission for reuse must be granted by Cambridge University Press in the first instance.
open_access (DINI-Set):open_access
faculties:Fakultät für Mathematik
Licence (German):License LogoNationale Lizenz

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