On nearly radial marginals of high-dimensional probability measures

DOI10.4171/JEMS/213zbMath1200.28015arXiv0810.4700MaRDI QIDQ973862

Bo'az Klartag

Publication date: 26 May 2010

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.4700

zbMATH Keywords

Dvoretzky's theoremhigh-dimensional measuresradially-symmetric.spherically-symmetric

Mathematics Subject Classification ID

Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Nonstandard measure theory (28E05)

Related Items (13)

Super-Gaussian Directions of Random Vectors ⋮ ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES ⋮ Colourful categories ⋮ Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures ⋮ Approximations of convex bodies by measure-generated sets ⋮ Cone-volume measure of general centered convex bodies ⋮ Isotropic measures and stronger forms of the reverse isoperimetric inequality ⋮ An improvement on the Rado bound for the centerline depth ⋮ $𝜓_{𝛼}$-estimates for marginals of log-concave probability measures ⋮ A center transversal theorem for an improved Rado depth ⋮ Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ On the Gaussian behavior of marginals and the mean width of random polytopes

Cites Work

• A Berry-Esseen type inequality for convex bodies with an unconditional basis
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• Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
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• Approximation of zonoids by zonotopes
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• A note on subgaussian estimates for linear functionals on convex bodies
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