Poincaré inequalities and dimension free concentration of measure

Nathael Gozlan

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 3, page 708-739
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Gozlan, Nathael. "Poincaré inequalities and dimension free concentration of measure." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 708-739. <http://eudml.org/doc/241624>.

@article{Gozlan2010,
abstract = {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.},
author = {Gozlan, Nathael},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Poincaré inequality; concentration of measure; transportation-cost inequalities; inf-convolution inequalities; logarithmic-Sobolev inequalities; super Poincaré inequalities},
language = {eng},
number = {3},
pages = {708-739},
publisher = {Gauthier-Villars},
title = {Poincaré inequalities and dimension free concentration of measure},
url = {http://eudml.org/doc/241624},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Gozlan, Nathael
TI - Poincaré inequalities and dimension free concentration of measure
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 3
SP - 708
EP - 739
AB - 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.
LA - eng
KW - Poincaré inequality; concentration of measure; transportation-cost inequalities; inf-convolution inequalities; logarithmic-Sobolev inequalities; super Poincaré inequalities
UR - http://eudml.org/doc/241624
ER -

References

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