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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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          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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              On choosing and bounding probability metrics

              Alison Gibbs, Francis Edward Su (2002)
              When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by statisticians and probabilists. We focus on these metrics because they are either well-known, commonly used, or admit practical bounding techniques. We summarize these relationships in a handy reference diagram, and also give examples to show how rates of convergence can depend on the metric chosen.
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                Author and article information

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                Publication date Created: 15 May 2018
                Article
                ArXiV ID: 1805.06107
                SO-VID: 1b00ccf7-6bae-4ac5-afdd-61a807c88985
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments 24 pages
                Categories math.AP math.PR

                ScienceOpen disciplines: Analysis,Probability
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                ScienceOpen disciplines: Analysis, Probability

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