Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ℝ</mml:mi></mml:math>

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.

Locations

• Annales mathématiques Blaise Pascal - View - PDF
• arXiv (Cornell University) - View