Archive for Rational Mechanics and Analysis

, Volume 161, Issue 3, pp 257–269 | Cite as

Some Applications of Mass Transport to Gaussian-Type Inequalities

  • Dario Cordero-Erausquin

Abstract

As discovered by Brenier, mapping through a convex gradient gives the optimal transport in ℝn. In the present article, this map is used in the setting of Gaussian-like measures to derive an inequality linking entropy with mass displacement by a straightforward argument. As a consequence, logarithmic Sobolev and transport inequalities are recovered. Finally, a result of Caffarelli on the Brenier map is used to obtain Gaussian correlation inequalities.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dario Cordero-Erausquin
    • 1
  1. 1.Equipe d'Analyse et de Mathématiques Appliquées¶Université de Marne-la-Vallée¶77454 Marne-la-Vallée Cedex 2¶France¶e-mail:cordero@math.univ-mlv.frFR

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