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Modified Logarithmic Sobolev Inequalities on \(\mathbb{R}\)

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Abstract

We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.

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Authors and Affiliations

  1. Institut de Mathématiques, Université Paul Sabatier, 31062, Toulouse cedex 09, France

    F. Barthe

  2. Laboratoire d’Analyse et Mathématiques Appliquées- UMR 8050, Universités de Marne la Vallée et de Paris 12-Val-de-Marne, Boulevard Descartes, Cité Descartes, Champs sur Marne, 77454, Marne la Vallée Cedex 2, France

    C. Roberto

Authors
  1. F. Barthe
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  2. C. Roberto
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Correspondence to C. Roberto.

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Barthe, F., Roberto, C. Modified Logarithmic Sobolev Inequalities on \(\mathbb{R}\) . Potential Anal 29, 167–193 (2008). https://doi.org/10.1007/s11118-008-9093-5

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  • DOI: https://doi.org/10.1007/s11118-008-9093-5

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