Transport proofs of weighted Poincaré inequalities for log-concave distributions

2014/07/11 by Cordero-Erausquin, Dario, Gozlan, Nathael
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1407.3217

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.

Related

• Transport inequalities for log-concave measures, quantitative forms and applications
• On the Poincaré constant of log-concave measures
• Geometric and Functional Inequalities for Log-concave Probability Sequences
• Weighted Poincaré inequalities, concentration inequalities and tail bounds related to the Stein kernels in dimension one
• Improved log-concavity for rotationally invariant measures of symmetric convex sets