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arXiv · 2501.08614

Expected extremal area of facets of random polytopes

Brett Leroux·Luis Rademacher·Carsten Schütt·Elisabeth M. Werner
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Abstract

We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in $\mathbb{R}^n$. 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.

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Brett Leroux, Luis Rademacher, Carsten Schütt, Elisabeth M. Werner. 2025-01-15. Expected extremal area of facets of random polytopes. https://arxiv.org/abs/2501.08614

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