Asymptotic expected T$T$‐functionals of random polytopes with applications to Lp$L_p$ surface areas

An asymptotic formula is proved for the expected T$T$‐functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in Rn$\mathbb {R}^n$ according to an arbitrary positive continuous density. As an application, the approximation of the...

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Bibliographic Details
Published in:Mathematische Nachrichten 2024-03, Vol.297 (3), p.914-931
Main Authors: Hoehner, Steven, Li, Ben, Roysdon, Michael, Thäle, Christoph
Format: Article
Language:English
Subjects:
Asymptotic properties
Convexity
Lp$L_p$ surface area
Polytopes
random polytope
stochastic geometry
Surface area
T$T$‐functional
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Summary:An asymptotic formula is proved for the expected T$T$‐functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in Rn$\mathbb {R}^n$ according to an arbitrary positive continuous density. As an application, the approximation of the sphere by random polytopes in terms of Lp$L_p$ surface area differences is discussed.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200495