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arXiv · 1412.1519

Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$

David Zimmermann
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Abstract

In a 2013 paper, the author showed that the convolution of a compactly supported measure on the real line with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). In a 2014 paper, the author gave bounds for the optimal constants in these LSIs. In this paper, we give a simpler, elementary proof of this result.

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David Zimmermann. 2014-12-03. Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on $\mathbb{R}$. https://arxiv.org/abs/1412.1519

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