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FUNCTIONAL INEQUALITIES FOR TWO-LEVEL CONCENTRATION

Abstract : Probability measures satisfying a Poincaré inequality are known to enjoy a dimension free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension free concentration property , known as two-level concentration. We show that a similar phenomenon occurs for the Latała-Oleszkiewicz inequalities, which were devised to uncover dimension free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.
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https://hal.archives-ouvertes.fr/hal-02281782
Contributeur : Franck Barthe <>
Soumis le : lundi 9 septembre 2019 - 14:53:48
Dernière modification le : jeudi 5 mars 2020 - 15:08:04
Document(s) archivé(s) le : vendredi 7 février 2020 - 02:43:49

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tlse20190909.pdf
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  • HAL Id : hal-02281782, version 1

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Franck Barthe, Michał Strzelecki. FUNCTIONAL INEQUALITIES FOR TWO-LEVEL CONCENTRATION. 2019. ⟨hal-02281782v1⟩

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