Displaying similar documents to “On Talagrand's deviation inequalities for product measures”

Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré

Pierre-André Zitt (2008)

ESAIM: Probability and Statistics

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In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [- (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants...

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki (2015)

Studia Mathematica

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We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev...

On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities

Djalil Chafaï, Florent Malrieu (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter...

New means of Cauchy's type.

Anwar, Matloob, Pečarić, J. (2008)

Journal of Inequalities and Applications [electronic only]

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