Limit theorems for random polytopes with vertices on convex surfaces

2017/06/09 by Turchi, Nicola, Wespi, Florian · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.02944

Abstract

The random polytope K_n, defined as the convex hull of n points chosen uniformly at random on the boundary of a smooth convex body, is considered. Proofs for lower and upper variance bounds, strong laws of large numbers and central limit theorems for the intrinsic volumes of K_n are presented. A normal approximation bound from Stein's method and estimates for surface bodies are among the involved tools.

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• Central limit theorems for random boundary polytopes

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