Displaying similar documents to “Levels of concentration between exponential and Gaussian”

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...

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...

An isoperimetric inequality on the ℓp balls

Sasha Sodin (2008)

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

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The normalised volume measure on the unit ball (1≤≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure is at least log(1/), where =min(, 1−).