%0 Unpublished work %T Stability for the logarithmic Sobolev inequality %+ CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) %+ Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) %A Brigati, Giovanni %A Dolbeault, Jean %A Simonov, Nikita %Z Marie Sklodowska-Curie grant agreement No 754362 %8 2023-03-22 %D 2023 %K Logarithmic Sobolev inequality %K stability %K log-concavity %K heat flow %K entropy %K carré du champ %Z 39B62, 47J20, 49J40, 35A23, 35K85 %Z Mathematics [math]Preprints, Working Papers, ... %X This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality. Our approach covers several cases involving the strongest possible norm with the optimal exponent, under constraints. Explicit constants are obtained. The strategy of proof relies on entropy methods and the Ornstein-Uhlenbeck flow. %G English %2 https://hal.science/hal-04042046/document %2 https://hal.science/hal-04042046/file/BDS2023-LSI.pdf %L hal-04042046 %U https://hal.science/hal-04042046 %~ CNRS %~ UNIV-DAUPHINE %~ INSMI %~ CEREMADE %~ LJLL %~ PSL %~ SORBONNE-UNIVERSITE %~ SORBONNE-UNIV %~ SU-SCIENCES %~ UNIV-PARIS %~ UNIVERSITE-PARIS %~ UP-SCIENCES %~ UNIV-DAUPHINE-PSL %~ SU-TI %~ ALLIANCE-SU