English

Expected extremal area of facets of random polytopes

Probability 2025-01-16 v1 Metric Geometry

Abstract

We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in Rn\mathbb{R}^n. The extremal properties of interest are the expected values of the maximum and minimum surface area among facets. We determine the asymptotic growth in every fixed dimension, up to absolute constants.

Keywords

Cite

@article{arxiv.2501.08614,
  title  = {Expected extremal area of facets of random polytopes},
  author = {Brett Leroux and Luis Rademacher and Carsten Schütt and Elisabeth M. Werner},
  journal= {arXiv preprint arXiv:2501.08614},
  year   = {2025}
}