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February 2017 Transport proofs of weighted Poincaré inequalities for log-concave distributions
Dario Cordero-Erausquin, Nathael Gozlan
Bernoulli 23(1): 134-158 (February 2017). DOI: 10.3150/15-BEJ739


We prove, using optimal transport tools, weighted Poincaré 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. "Transport proofs of weighted Poincaré inequalities for log-concave distributions." Bernoulli 23 (1) 134 - 158, February 2017.


Received: 1 July 2014; Revised: 1 May 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 1378.60044
MathSciNet: MR3556769
Digital Object Identifier: 10.3150/15-BEJ739

Keywords: Log-concave measures , Transport inequalities , weighted Poincaré inequalities

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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