# Transport proof of weighted Poincaré inequalities for log-concave probability measures.

## Nathael Gozlan

### (Univ. Paris Est.)

Date: Oct 28, 2014, time: 09:55

Abstract. We prove, using optimal transport tools, weighted Poincar 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. Joint work with D. Cordero-Erausquin.