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.
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⟩
