Concentration of mass and central limit properties of isotropic convex bodies

DOI10.1090/S0002-9939-04-07757-3zbMath1064.52005OpenAlexW1569358184MaRDI QIDQ4825649

Grigoris Paouris

Publication date: 28 October 2004

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-04-07757-3

zbMATH Keywords

central limit theoremconcentration of volumeisotropic convex body

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) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Large deviations for high-dimensional random projections of \(\ell_p^n\)-balls ⋮ A central limit theorem for convex sets ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ On the geometry of random convex sets between polytopes and zonotopes ⋮ A note on volume thresholds for random polytopes ⋮ Concentration of mass on isotropic convex bodies

Cites Work

• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• The subindependence of coordinate slabs in \(l_p^n\) balls
• Asymptotics of cross sections for convex bodies
• Isoperimetric problems for convex bodies and a localization lemma
• The central limit problem for convex bodies
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)
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