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• W2130401121 abstract "We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal.6, 587–600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities. Conversely, Talagrand's inequality implies a logarithmic Sobolev inequality if the density of the measure is approximately log-concave, in a precise sense. All constants are independent of the dimension and optimal in certain cases. The proofs are based on partial differential equations and an interpolation inequality involving the Wasserstein distance, the entropy functional, and the Fisher information." @default.
• W2130401121 created "2016-06-24" @default.
• W2130401121 creator A5021250887 @default.
• W2130401121 creator A5073872018 @default.
• W2130401121 date "2000-06-01" @default.
• W2130401121 modified "2023-10-14" @default.
• W2130401121 title "Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality" @default.
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• W2130401121 doi "https://doi.org/10.1006/jfan.1999.3557" @default.
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