A note on the deficit of the logarithmic Sobolev inequality
Volume 45 / 2018
Applicationes Mathematicae 45 (2018), 199-205
MSC: Primary 26D10; Secondary 39B72.
DOI: 10.4064/am2360-6-2018
Published online: 24 July 2018
Abstract
We obtain a new bound for the deficit of the logarithmic Sobolev inequality. The starting point is the Cauchy–Schwarz inequality and, with no further inequalities, we obtain an elementary proof of one well known version of the inequality with the Gaussian distribution. With a further Jensen inequality we obtain a new lower bound for the log-Sobolev inequality.
