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Modified logarithmic Sobolev inequalities and transportation inequalities
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  • Published: 15 March 2005

Modified logarithmic Sobolev inequalities and transportation inequalities

  • Ivan Gentil1,
  • Arnaud Guillin1 &
  • Laurent Miclo2 

Probability Theory and Related Fields volume 133, pages 409–436 (2005)Cite this article

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Abstract.

We present a class of modified logarithmic Sobolev inequality, interpolating between Poincaré and logarithmic Sobolev inequalities, suitable for measures of the type exp (−|x|α) or exp (−|x|α log β(2+|x|)) (α ∈]1,2[ and β ∈ ℝ) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincaré inequality. We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities.

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Authors and Affiliations

  1. Ceremade (UMR CNRS no. 7534), Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, Paris, Cédex 16, 75775, France

    Ivan Gentil & Arnaud Guillin

  2. Laboratoire d'Analyse, Topologie, Probabilités (UMR CNRS no. 6632), Université de Provence, 39, rue F. Joliot Curie, Marseille, cédex 13, 13453, France

    Laurent Miclo

Authors
  1. Ivan Gentil
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  2. Arnaud Guillin
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  3. Laurent Miclo
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Correspondence to Ivan Gentil.

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Gentil, I., Guillin, A. & Miclo, L. Modified logarithmic Sobolev inequalities and transportation inequalities. Probab. Theory Relat. Fields 133, 409–436 (2005). https://doi.org/10.1007/s00440-005-0432-9

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  • Received: 16 May 2004

  • Revised: 05 January 2005

  • Published: 15 March 2005

  • Issue Date: November 2005

  • DOI: https://doi.org/10.1007/s00440-005-0432-9

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Keywords

  • Transportation
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Common Property
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