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

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 according to an arbitrary positive continuous density. As an application, the approximation of the sphere by random polytopes in terms of surface area differences is discussed.