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Pré-Publication, Document De Travail Année : 2015

Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities

Ivan Gentil

Résumé

In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations.
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Dates et versions

hal-01171361 , version 1 (03-07-2015)
hal-01171361 , version 2 (05-10-2015)
hal-01171361 , version 3 (09-11-2016)
hal-01171361 , version 4 (12-03-2017)

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François Bolley, Ivan Gentil, Arnaud Guillin. Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. 2015. ⟨hal-01171361v2⟩
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