Poincaré inequality for non euclidean metrics and transportation cost inequalities on $\mathbb{R}^d$ - Laboratoire d'Analyse et de Mathématiques Appliquées
Pré-Publication, Document De Travail Année : 2007

Poincaré inequality for non euclidean metrics and transportation cost inequalities on $\mathbb{R}^d$

Résumé

In this paper, we consider Poincaré inequalities for non euclidean metrics on $\mathbb{R}^d$. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give different equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and infimum convolution inequalities. Workable sufficient conditions are given and a comparison is made with generalized Beckner-Latala-Oleszkiewicz inequalities.
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Dates et versions

hal-00163909 , version 1 (19-07-2007)

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Nathael Gozlan. Poincaré inequality for non euclidean metrics and transportation cost inequalities on $\mathbb{R}^d$. 2007. ⟨hal-00163909⟩
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