Displaying similar documents to “An isoperimetric inequality on the ℓp balls”

On the volume of intersection of three independent Wiener sausages

M. van den Berg (2010)

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

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Let be a compact, non-polar set in ℝ, ≥3 and let ()={ ()+: 0≤≤, ∈} be Wiener sausages associated to independent brownian motions , =1, 2, 3 starting at 0. The expectation of volume of ⋂=13 () with respect to product measure is obtained in terms of the equilibrium measure of in the limit of large .

Potential confinement property of the parabolic Anderson model

Gabriela Grüninger, Wolfgang König (2009)

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

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We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in ℤ. We use i.i.d. potentials :ℤ→ℝ in the third universality class, namely the class of , in the classification of van der Hofstad, König and Mörters [ (2006) 307–353]. This class consists of potentials whose logarithmic moment generating function is regularly varying with parameter =1, but do not belong to the class of so-called double-exponentially distributed potentials...

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...

New means of Cauchy's type.

Anwar, Matloob, Pečarić, J. (2008)

Journal of Inequalities and Applications [electronic only]

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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...