Limit theorems for random polytopes with vertices on convex surfaces

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

paper · pdf · doi:10.48550/arxiv.1706.02944

arxiv created 2017/06/09 · arxiv updated 2017/06/12

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.

Cited by

• Central limit theorems for random boundary polytopes

Related

• Central limit theorems for random polytopes in a smooth convex set
• Random polytopes: central limit theorems for intrinsic volumes
• Random inscribed polytopes in projective geometries
• Central limit theorems for random boundary polytopes
• The convex hull of random points on the boundary of a simple polytope