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      Deficit Estimates for the Logarithmic Sobolev Inequality

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          Abstract

          We identify sharp spaces and prove quantitative and non-quantitative stability results for the logarithmic Sobolev inequality involving Wasserstein and \(L^p\) metrics. The techniques are based on optimal transport theory and Fourier analysis. We also discuss a probabilistic approach.

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          Most cited references 15

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          Topics in Optimal Transportation

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            Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

             F Otto,  C Villani (2000)
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              Logarithmic Sobolev Inequalities

               Leonard Gross (1976)
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                Author and article information

                Journal
                15 May 2018
                Article
                1805.06107

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                24 pages
                math.AP math.PR

                Analysis, Probability

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