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

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

2007-07-19

arxiv.org/abs/0707.2834v1

Ann. Inst. Henri Poincar\'e Probab. Stat. 46 (2010), no. 3, 708-739

Mathematics

Probability

Scientific paper

10.1214/09-AIHP209

In this paper, we consider Poincar\'e 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 Poincar\'e 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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