From dimension free concentration to Poincaré inequality

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.
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Contributor : Nathael Gozlan <>
Submitted on : Tuesday, October 8, 2013 - 11:01:33 PM
Last modification on : Thursday, July 18, 2019 - 3:00:05 PM
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  • HAL Id : hal-00823733, version 2
  • ARXIV : 1305.4331

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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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