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

Steven Hoehner; Ben Li; Michael Roysdon; Christoph Thäle

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arXiv · 2202.01353

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

Steven Hoehner·Ben Li·Michael Roysdon·Christoph Thäle

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Abstract

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

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Steven Hoehner, Ben Li, Michael Roysdon, Christoph Thäle. 2022-02-03. Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas. https://arxiv.org/abs/2202.01353

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