A characterization of a class of convex log-Sobolev inequalities on the real line

DOI10.1214/17-AIHP865zbMath1403.60022arXiv1702.04698MaRDI QIDQ1633917

Yan Shu, Michał Strzelecki

Publication date: 21 December 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04698

zbMATH Keywords

convex functionsconcentration of measurelog-Sobolev inequalityweak transport-entropy inequalities

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Convexity of real functions in one variable, generalizations (26A51) Inequalities involving derivatives and differential and integral operators (26D10)

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Cites Work

• Unnamed Item
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• Transport-entropy inequalities on the line
• Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution
• Modified logarithmic Sobolev inequalities on \(\mathbb{R}\)
• Modified logarithmic Sobolev inequalities in null curvature
• Some deviation inequalities
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Discrete isoperimetric and Poincaré-type inequalities
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Hypercontractivity of Hamilton-Jacobi equations.
• Comment on ``Hypercontractivity of Hamilton-Jacobi equations by S. G. Bobkov, I. Gentil and M. Ledoux.
• Characterization of a class of weak transport-entropy inequalities on the line
• Transportation cost for Gaussian and other product measures
• A note on the convex infimum convolution inequality
• Kantorovich duality for general transport costs and applications
• Logarithmic Sobolev inequalities for finite Markov chains
• Modified logarithmic Sobolev inequalities and transportation inequalities
• Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions
• Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses
• Logarithmic Sobolev Inequalities
• Sobolev inequalities for probability measures on the real line
• Analysis and Geometry of Markov Diffusion Operators
• Optimal Transport