Transport proofs of weighted Poincaré inequalities for log-concave distributions

Dario Cordero-Erausquin (1) , Nathael Gozlan (2, 3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Laboratoire d'Analyse et de Mathématiques Appliquées
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

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