no. G12
Article de recherche - Probabilités
Stochastic proof of the sharp symmetrized Talagrand inequality
[Une preuve stochastique de l’inégalité de Talagrand symétrisée optimale]
Courtade, Thomas A.1  ; Fathi, Max2, 3, 4 ; Mikulincer, Dan5
1Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720 USA
2Université Paris Cité and Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions and Laboratoire de Probabilités, Statistique et Modélisation, F-75013 Paris, France
3DMA, École normale supérieure, Université PSL, CNRS, 75005 Paris, France
4Institut Universitaire de France
5Department of Mathematics, MIT, Cambridge, MA 02139 USA
Comptes Rendus. Mathématique, Tome 362 (2024) no. G12, pp. 1779-1784

A new proof of the sharp symmetrized form of Talagrand’s transport-entropy inequality is given. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed martingale representations.

Nous donnons une nouvelle preuve de la version symétrisée de l’inégalité de transport-entropie de Talagrand avec constante optimale. En comparaison avec d’autres preuves stochastiques d’inégalités fonctionnelles gaussiennes, l’élément nouveau ici est l’utilisation d’un couplage induit par un retournement du temps sur des représentations de martingales.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/crmath.681
Classification : 60H30, 39B62, 52A40
Keywords: Transport inequalities, Gaussian inequalities, Blaschke–Santaló inequality, Martingale representations
Mots-clés : Inégalités de transport, inégalités Gaussiennes, inégalité de Blaschke–Santaló, représentations de martingales

Courtade, Thomas A.  1   ; Fathi, Max  2 , 3 , 4   ; Mikulincer, Dan  5

1 Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720 USA
2 Université Paris Cité and Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions and Laboratoire de Probabilités, Statistique et Modélisation, F-75013 Paris, France
3 DMA, École normale supérieure, Université PSL, CNRS, 75005 Paris, France
4 Institut Universitaire de France
5 Department of Mathematics, MIT, Cambridge, MA 02139 USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Courtade, Thomas A. and Fathi, Max and Mikulincer, Dan},
     title = {Stochastic proof of the sharp symmetrized {Talagrand} inequality},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1779--1784},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {G12},
     doi = {10.5802/crmath.681},
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     url = {https://www.numdam.org/articles/10.5802/crmath.681/}
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Courtade, Thomas A.; Fathi, Max; Mikulincer, Dan. Stochastic proof of the sharp symmetrized Talagrand inequality. Comptes Rendus. Mathématique, Tome 362 (2024) no. G12, pp. 1779-1784. doi: 10.5802/crmath.681

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