The symmetric property (\tau ) for the Gaussian measure
Résumé
We give a proof, based on the Poincaré inequality, of the symmetric property (τ) for the Gaussian measure. If f : R d → R is continuous, bounded from below and even, we define Hf (x) = inf y f (x + y) + 1 2 |y| 2 and we have ∫ e^−f dγ d ∫ e Hf dγ d ≤ 1. This property is equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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