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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.

### Most cited references15

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### Topics in Optimal Transportation

(2003)
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### Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

(2000)
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### Logarithmic Sobolev Inequalities

(1976)
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### Author and article information

###### Journal
15 May 2018
###### Article
1805.06107