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arXiv · 1407.3217

Transport proofs of weighted Poincaré inequalities for log-concave distributions

Dario Cordero-Erausquin·Nathael Gozlan
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Abstract

We prove, using optimal transport tools, weighted Poincar'e inequalities for log-concave random vectors satisfying some centering conditions. We recover by this way similar results by Klartag and Barthe-Cordero-Erausquin for log-concave random vectors with symmetries. In addition, we prove that the variance conjecture is true for increments of log-concave martingales.

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Dario Cordero-Erausquin, Nathael Gozlan. 2014-07-11. Transport proofs of weighted Poincaré inequalities for log-concave distributions. https://arxiv.org/abs/1407.3217

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