# From dimension free concentration to Poincaré inequality

1 Laboratoire d'Analyse et de Mathématiques Appliquées
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : We prove that a probability measure on an abstract metric space satisfies a non trivial dimension free concentration inequality for the $\ell_2$ metric if and only if it satisfies the Poincaré inequality.
Document type :
Journal articles
Domain :

Cited literature [40 references]

https://hal-upec-upem.archives-ouvertes.fr/hal-00823733
Contributor : Nathael Gozlan <>
Submitted on : Tuesday, October 8, 2013 - 11:01:33 PM
Last modification on : Thursday, July 18, 2019 - 3:00:05 PM
Long-term archiving on : Friday, April 7, 2017 - 8:33:07 AM

### Files

Poincare-JMPA-submitted.pdf
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### Identifiers

• HAL Id : hal-00823733, version 2
• ARXIV : 1305.4331

### Citation

Nathael Gozlan, Cyril Roberto, Paul-Marie Samson. From dimension free concentration to Poincaré inequality. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2015. ⟨hal-00823733v2⟩

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