Transport proofs of weighted Poincaré inequalities for log-concave distributions

Dario Cordero-Erausquin 1 Nathael Gozlan 2
1 Institut de Mathmatiques de Jussieu
IMJ - Institut de Mathématiques de Jussieu
2 Laboratoire d'Analyse et de Mathématiques Appliquées
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
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.
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  • HAL Id : hal-01023065, version 1
  • ARXIV : 1407.3217

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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⟩

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