Limit theorems for random polytopes with vertices on convex surfaces
Probability
2017-06-12 v1 Metric Geometry
Abstract
The random polytope , defined as the convex hull of 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 are presented. A normal approximation bound from Stein's method and estimates for surface bodies are among the involved tools.
Cite
@article{arxiv.1706.02944,
title = {Limit theorems for random polytopes with vertices on convex surfaces},
author = {Nicola Turchi and Florian Wespi},
journal= {arXiv preprint arXiv:1706.02944},
year = {2017}
}