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• W239225224 abstract "We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian measure restricted to probability densities which satisfy a Poincare inequality. The result implies a lower bound on the deficit in terms of the quadratic Kantorovich-Wasserstein distance. We similarly investigate the deficit in the Talagrand quadratic transportation cost inequality this time by means of an ${rm L}^1$-Kantorovich-Wasserstein distance, optimal for product measures, and deduce a lower bound on the deficit in the logarithmic Sobolev inequality in terms of this metric. Applications are given in the context of the Bakry-Emery theory and the coherent state transform. The proofs combine tools from semigroup and heat kernel theory and optimal mass transportation." @default.
• W239225224 created "2016-06-24" @default.
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• W239225224 date "2014-10-25" @default.
• W239225224 modified "2023-10-01" @default.
• W239225224 title "Quantitative logarithmic Sobolev inequalities and stability estimates" @default.
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• W239225224 hasPublicationYear "2014" @default.
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