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A Feynman-Kac approach for Logarithmic Sobolev Inequalities

Abstract : This note presents a method based on Feynman-Kac semigroups for logarithmic Sobolev inequalities. It follows the recent work of Bonnefont and Joulin on intertwining relations for diffusion operators, formerly used for spectral gap inequalities, and related to perturbation techniques. In particular, it goes beyond the Bakry-Émery criterion and allows to investigate high-dimensional effects on the optimal logarithmic Sobolev constant. The method is illustrated on particular examples (namely Subbotin distributions and double-well potentials), for which explicit dimension-free bounds on the latter constant are provided. We eventually discuss a brief comparison with the Holley-Stroock approach.
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https://hal.archives-ouvertes.fr/hal-02464170
Contributor : Clément Steiner <>
Submitted on : Tuesday, June 8, 2021 - 3:00:17 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:11 AM

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  • HAL Id : hal-02464170, version 2
  • ARXIV : 2002.01167

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Clément Steiner. A Feynman-Kac approach for Logarithmic Sobolev Inequalities. 2021. ⟨hal-02464170v2⟩

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