Deficit Estimates for the Logarithmic Sobolev Inequality

Published 16 May 2018 in math.AP and math.PR | (1805.06107v1)

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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