On the isotropy constant of random convex sets

DOI10.1090/S0002-9939-08-09487-2zbMath1157.52005arXiv0707.1570OpenAlexW1969372199MaRDI QIDQ3522330

David Alonso-Gutiérrez

Publication date: 1 September 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1570

zbMATH Keywords

isotropic positionisotropy constant

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (14)

Gaussian polytopes: a cumulant-based approach ⋮ On the isotropy constant of projections of polytopes ⋮ Facets of spherical random polytopes ⋮ A geometric analysis of subspace clustering with outliers ⋮ Dimensionality-reduced subspace clustering ⋮ Estimating support functions of random polytopes via Orlicz norms ⋮ On the isotropic constant of random polytopes ⋮ The minimal volume of simplices containing a convex body ⋮ On the isotropic constant of random polytopes ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ The isotropic constant of random polytopes with vertices on convex surfaces ⋮ Continuous quantitative Helly-type results ⋮ Poisson polyhedra in high dimensions ⋮ Asymptotic shape of the convex hull of isotropic log-concave random vectors

Cites Work

• On the hyperplane conjecture for random convex sets
• On convex perturbations with a bounded isotropic constant
• The isotropy constants of the Schatten classes are bounded
• Smallest singular value of random matrices and geometry of random polytopes
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