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