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arXiv · 1805.06107

Deficit Estimates for the Logarithmic Sobolev Inequality

Emanuel Indrei·Daesung Kim
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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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Emanuel Indrei, Daesung Kim. 2018-05-16. Deficit Estimates for the Logarithmic Sobolev Inequality. https://arxiv.org/abs/1805.06107

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