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arXiv · 1305.4331

From dimension free concentration to Poincar\'e inequality

Nathael Gozlan·Cyril Roberto·Paul-Marie Samson
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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 Poincar\'e inequality.

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Nathael Gozlan, Cyril Roberto, Paul-Marie Samson. 2013-05-19. From dimension free concentration to Poincar\'e inequality. https://arxiv.org/abs/1305.4331

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