In this paper, we consider Poincaré inequalities for non-Euclidean metrics on ℝd. 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 equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions are given and a comparison is made with super Poincaré inequalities.
Publié le : 2010-08-15
Classification:
Poincaré inequality,
Concentration of measure,
Transportation-cost inequalities,
Inf-convolution inequalities,
Logarithmic-Sobolev inequalities,
Super Poincaré inequalities,
60E15,
26D10
@article{1281100396,
author = {Gozlan, Nathael},
title = {Poincar\'e inequalities and dimension free concentration of measure},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 708-739},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100396}
}
Gozlan, Nathael. Poincaré inequalities and dimension free concentration of measure. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 708-739. http://gdmltest.u-ga.fr/item/1281100396/