A Stein deficit for the logarithmic Sobolev inequality
Probability
2017-08-02 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1602.08235,
title = {A Stein deficit for the logarithmic Sobolev inequality},
author = {Michel Ledoux and Ivan Nourdin and Giovanni Peccati},
journal= {arXiv preprint arXiv:1602.08235},
year = {2017}
}
Comments
22 pages