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<p>We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3153_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. 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.</p>

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Expected extremal area of facets of random polytopes

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Brett Leroux,
  • Luis Rademacher,
  • Carsten Schütt,
  • Elisabeth M. Werner

摘要

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