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

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  • Steven Hoehner
  • Ben Li
  • Michael Roysdon
  • Christoph Thäle

Abstract

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.

Suggested Citation

  • Steven Hoehner & Ben Li & Michael Roysdon & Christoph Thäle, 2024. "Asymptotic expected T$T$‐functionals of random polytopes with applications to Lp$L_p$ surface areas," Mathematische Nachrichten, Wiley Blackwell, vol. 297(3), pages 914-931, March.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:3:p:914-931
    DOI: 10.1002/mana.202200495
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