Year: 2025
Type: preprint
Abstract: Approximate a smooth convex body $K$ with nonvanishing curvature by the convex hull of $n$ independent random points sampled from its boundary $\partial K$. In case the points are distributed according to the optimal density, we prove that the rescaled approximation error in Hausdorff distance tends to a Gumbel distributed random variable. The proof is based on an asymptotic relation to covering properties of random geodesic balls on $\partial K$ and on a limit theorem due to Janson.
Source: arXiv (Cornell University)
Author: Sonnleitner, Mathias
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077674314
Cites:
Cited by:
Related to: