Order statistics and concentration of \(l_r\) norms for log-concave vectors

DOI10.1016/j.jfa.2011.02.013zbMath1217.60016arXiv1011.6610OpenAlexW2017947969MaRDI QIDQ544018

Rafał Latała

Publication date: 14 June 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6610

zbMATH Keywords

order statisticslog-concave measuresconcentration of volume

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

Related Items (8)

Order statistics of vectors with dependent coordinates, and the Karhunen-Loève basis ⋮ On generic chaining and the smallest singular value of random matrices with heavy tails ⋮ On the Poincaré Constant of Log-Concave Measures ⋮ Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body ⋮ Geometry of log-concave ensembles of random matrices and approximate reconstruction ⋮ Sparse equisigned PCA: algorithms and performance bounds in the noisy rank-1 setting ⋮ Weak and strong moments of ℓᵣ-norms of log-concave vectors ⋮ Modified Paouris Inequality

Cites Work

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• A Berry-Esseen type inequality for convex bodies with an unconditional basis
• Concentration of mass on convex bodies
• On the role of convexity in isoperimetry, spectral gap and concentration
• Convex measures on locally convex spaces
• Isoperimetric problems for convex bodies and a localization lemma
• SPECTRAL GAP FOR SOME INVARIANT LOG‐CONCAVE PROBABILITY MEASURES
• Tail and moment estimates for sums of independent random vectors with logarithmically concave tails

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