The expected number of facets and the typical facet height of the convex hull of n uniform points on S^{d-1} are determined asymptotically in every regime where n and d tend to infinity.
Volume degeneracy of t he typical cell and the chord length distribution for Poisson-Voronoi tessellations in high dimensions
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Facets of spherical random polytopes
The expected number of facets and the typical facet height of the convex hull of n uniform points on S^{d-1} are determined asymptotically in every regime where n and d tend to infinity.