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arXiv · 2603.22224

Higher moments of intrinsic volumes of random beta-prime polytopes

Ferenc Fodor·Balázs Grünfelder·Péter Kevei
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Abstract

We consider beta-prime polytopes, i.e., the convex hulls of iid random points chosen according to beta-prime distributions in $\mathbb{R}^d$. After suitable scaling, beta-prime polytopes converge in distribution to the convex hulls of Poisson point processes with power-law intensity functions. We prove moment convergence for the volume and all intrinsic volumes. Beta-prime polytopes are the push-forwards of spherical random polytopes on the upper open half-sphere of the unit sphere $S^d\subset \mathbb{R}^{d+1}$. We prove convergence of moments of the spherical volume difference of the half-sphere and the spherical random polytopes.

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Ferenc Fodor, Balázs Grünfelder, Péter Kevei. 2026-03-23. Higher moments of intrinsic volumes of random beta-prime polytopes. https://arxiv.org/abs/2603.22224

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