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arXiv · 1302.4910

A quantitative log-Sobolev inequality for a two parameter family of functions

Emanuel Indrei·Diego Marcon
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Abstract

We prove a sharp, dimension-free stability result for the classical logarithmic Sobolev inequality for a two parameter family of functions. Roughly speaking, our family consists of a certain class of log $C^{1,1}$ functions. Moreover, we show how to enlarge this space at the expense of the dimensionless constant and the sharp exponent. As an application we obtain new bounds on the entropy.

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Emanuel Indrei, Diego Marcon. 2013-02-20. A quantitative log-Sobolev inequality for a two parameter family of functions. https://arxiv.org/abs/1302.4910

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