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

Steven Hoehner, Ben Li, Michael Roysdon and Christoph Thäle

Mathematische Nachrichten, 2024, vol. 297, issue 3, 914-931

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.

Date: 2024
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