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Article Dans Une Revue International Mathematics Research Notices Année : 2022

THE DEFICIT IN THE GAUSSIAN LOG-SOBOLEV INEQUALITY AND INVERSE SANTALO INEQUALITIES

Résumé

We establish dual equivalent forms involving relative entropy, Fisher information and optimal transport costs of inverse Santaló inequalities. We show in particular that the Mahler conjecture is equivalent to some dimensional lower bound on the deficit in the Gaussian logarithmic Sobolev inequality. We also derive from existing results on inverse Santaló inequalities some sharp lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality.
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Dates et versions

hal-02895573 , version 1 (09-07-2020)
hal-02895573 , version 2 (27-03-2021)

Identifiants

Citer

Nathaël Gozlan. THE DEFICIT IN THE GAUSSIAN LOG-SOBOLEV INEQUALITY AND INVERSE SANTALO INEQUALITIES. International Mathematics Research Notices, 2022, 2022 (17), pp.12940-12983. ⟨10.1093/imrn/rnab087⟩. ⟨hal-02895573v2⟩
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