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.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-02281782
Contributeur : Franck Barthe <>
Soumis le : lundi 9 septembre 2019 - 14:53:48
Dernière modification le : vendredi 11 octobre 2019 - 20:22:43

Fichier

tlse20190909.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-02281782, version 1

Citation

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

Partager

Métriques

Consultations de la notice

26

Téléchargements de fichiers

53