On determinants and the volume of random polytopes in isotropic convex bodies

DOI10.1007/s10711-010-9462-2zbMath1211.52006OpenAlexW2048340541MaRDI QIDQ605058

Peter Pivovarov

Publication date: 23 November 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-010-9462-2

zbMATH Keywords

zonotoperandom polytopeHadamard's inequalityisotropic convex bodyrandom determinant

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Asymptotic theory of convex bodies (52A23)

Related Items (12)

On the measure of anchored Gaussian simplices, with applications to multivariate medians ⋮ Unnamed Item ⋮ Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body ⋮ Small-ball probabilities for the volume of random convex sets ⋮ On the isotropic constant of random polytopes ⋮ The minimal volume of simplices containing a convex body ⋮ Asymptotic estimates for the largest volume ratio of a convex body ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ Approximate Voronoi cells for lattices, revisited ⋮ Proof of a conjecture of Bárány, Katchalski and Pach ⋮ On the volume bound in the Dvoretzky-Rogers lemma ⋮ Threshold phenomena for high-dimensional random polytopes

Cites Work

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• Random p-content of a p-parallelotope in Euclidean n-space
• Small ball probability estimates for log-concave measures
• Isotropic random simplices
• RANDOM POINTS IN ISOTROPIC UNCONDITIONAL CONVEX BODIES

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