Facets of spherical random polytopes

Gilles Bonnet and Eliza O'Reilly

Mathematische Nachrichten, 2022, vol. 295, issue 10, 1901-1933

Abstract: Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit sphere in Rd$\mathbb {R}^d$ are studied. A particular focus is given on the height of the facets as well as the expected number of facets as the dimension increases. Regimes for n and d with different asymptotic behavior of these quantities are identified and asymptotic formulas in each case are established. Extensions of several known results in fixed dimension to the case where dimension tends to infinity are described.

Date: 2022
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