Mass Transportation Proofs of Free Functional Inequalities, and Free Poincare Inequalities

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dc.creatorLedoux, Michel
dc.creatorPopescu, Ionel
dc.date2009-03-22
dc.date.accessioned2026-07-07T12:55:36Z
dc.date.available2026-07-07T12:55:36Z
dc.descriptionThis work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the transportation, Log-Sobolev, HWI interpolation and Brunn-Minkowski inequalities for strictly convex potentials. Sharp constants and some extended versions are put forward. The paper also addresses two versions of free Poincaré inequalities and their interpretation in terms of spectral properties of Jacobi operators. The last part establishes the corresponding inequalities for measures on $\R_{+}$ with the reference example of the Marcenko-Pastur distribution.
dc.descriptionThis paper will apear in Journal of Fucntional Analysis
dc.identifierhttps://arxiv.org/abs/0903.3761
dc.identifierhttp://arxiv.org/abs/0903.3761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224307
dc.subjectFunctional Analysis
dc.subjectProbability
dc.titleMass Transportation Proofs of Free Functional Inequalities, and Free Poincare Inequalities
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