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

Steven Hoehner; Ben Li; Michael Roysdon; Christoph Thäle

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

Probability 2023-08-02 v3 Metric Geometry

Authors: Steven Hoehner , Ben Li , Michael Roysdon , Christoph Thäle

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.

Keywords

random polytopes t-functional expected value euclidean unit sphere l_p surface area asymptotic formula

Cite

@article{arxiv.2202.01353,
  title  = {Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas},
  author = {Steven Hoehner and Ben Li and Michael Roysdon and Christoph Thäle},
  journal= {arXiv preprint arXiv:2202.01353},
  year   = {2023}
}

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20 pages

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

Abstract

Keywords

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