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arXiv · 1602.08235

A Stein deficit for the logarithmic Sobolev inequality

Michel Ledoux·Ivan Nourdin·Giovanni Peccati
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Abstract

We provide explicit lower bounds for the deficit in the Gaussian logarithmic Sobolev inequality in terms of differential operators that are naturally associated with the so-called Stein characterization of the Gaussian distribution. The techniques are based on a crucial use of the representation of the relative Fisher information, along the Ornstein-Uhlenbeck semigroup, in terms of the Minimal Mean-Square Error from information theory.

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Michel Ledoux, Ivan Nourdin, Giovanni Peccati. 2016-02-26. A Stein deficit for the logarithmic Sobolev inequality. https://doi.org/10.1007/s11425-016-0134-7

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