Second-order concentration on the sphere

DOI10.1142/S0219199716500589zbMath1373.60043arXiv1502.04178OpenAlexW2963029033MaRDI QIDQ5354378

Friedrich Götze, Sergey G. Bobkov, Gennadiy P. Chistyakov

Publication date: 1 September 2017

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.04178

zbMATH Keywords

logarithmic Sobolev inequalitiesconcentration of measure phenomenon

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Large deviations (60F10) Inequalities for sums, series and integrals (26D15)

Related Items

Concentration between Lévy’s inequality and the Poincaré inequality for log-concave densities, Modified log-Sobolev inequalities and two-level concentration, Moment estimates implied by modified log-Sobolev inequalities, Higher order concentration on Stiefel and Grassmann manifolds, Higher order concentration of measure, Second order concentration via logarithmic Sobolev inequalities, Concentration inequalities for bounded functionals via log-Sobolev-type inequalities, Poincaré inequalities and normal approximation for weighted sums, Modified log-Sobolev inequalities, Beckner inequalities and moment estimates, Normal approximation for weighted sums under a second-order correlation condition

Cites Work

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• Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order
• A Berry-Esseen type inequality for convex bodies with an unconditional basis
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• A new isoperimetric inequality for product measure and the tails of sums of independent random variables
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Logarithmic Sobolev inequalities and exponential integrability
• Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere
• Concentration of measure and isoperimetric inequalities in product spaces
• Variations on the Berry--Esseen Theorem
• Analysis and Geometry of Markov Diffusion Operators