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Transport proofs of weighted Poincaré inequalities for log-concave distributions

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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Contributor : Nathael Gozlan Connect in order to contact the contributor
Submitted on : Friday, July 11, 2014 - 2:35:16 PM
Last modification on : Saturday, January 15, 2022 - 4:06:31 AM
Long-term archiving on: : Saturday, October 11, 2014 - 12:40:31 PM


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  • HAL Id : hal-01023065, version 1
  • ARXIV : 1407.3217


Dario Cordero-Erausquin, Nathael Gozlan. Transport proofs of weighted Poincaré inequalities for log-concave distributions. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (1), pp.134 - 158. ⟨hal-01023065⟩



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