Variance lower bounds for geometric functionals of rotationally invariant log-concave random polytopes
Year: 2026
Type: preprint
Abstract: We establish variance lower bounds for the intrinsic volumes and the face numbers of random polytopes, generated by independent samples from rotationally invariant log-concave probability measures on $\mathbb{R}^d$ with full support. Our results extend the corresponding Gaussian lower bounds of Bárány and Vu and of Bárány and Thäle to this broader class of distributions. Our proof builds on the geometric construction introduced by Bárány and Vu, for which we develop an alternative treatment based on barycentric coordinates. We combine it with local variance estimates for both intrinsic volumes and the number of faces.
Source: arXiv (Cornell University)
Authors: Pafis, Minas, Pandis, Christos
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204209884