Modified logarithmic Sobolev inequalities in null curvature

DOI10.4171/RMI/493zbMath1123.26022arXivmath/0503585MaRDI QIDQ997816

Laurent Miclo, Ivan Gentil, Arnaud Guillin

Publication date: 7 August 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503585

zbMATH Keywords

Poincaré inequalityconcentration inequalitylog-concave measure

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Systems of functional equations and inequalities (39B72) Inequalities in real analysis (26D99)

Related Items (13)

A characterization of a class of convex log-Sobolev inequalities on the real line ⋮ Modified logarithmic Sobolev inequalities and transportation cost inequalities in \(\mathbb R^{n}\) ⋮ Moment estimates implied by modified log-Sobolev inequalities ⋮ Characterization of Talagrand's transport-entropy inequalities in metric spaces ⋮ A note on the modified log-Sobolev inequality ⋮ Weighted Nash inequalities ⋮ Characterization of Talagrand's like transportation-cost inequalities on the real line ⋮ Modified logarithmic Sobolev inequalities on \(\mathbb{R}\) ⋮ From super Poincaré to weighted log-Sobolev and entropy-cost inequalities ⋮ Mass transport and variants of the logarithmic Sobolev inequality ⋮ A new characterization of Talagrand's transport-entropy inequalities and applications ⋮ Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions ⋮ From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Cites Work

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• Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution
• Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Concentration of measure and isoperimetric inequalities in product spaces
• Modified logarithmic Sobolev inequalities and transportation inequalities
• Logarithmic Sobolev Inequalities
• Sobolev inequalities for probability measures on the real line
• Hardy's inequality with weights

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