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

2013/02/20 by Emanuel Indrei, Diego Marcon, Indrei, Emanuel +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.AP #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.1302.4910

14 pages

arxiv created 2013/02/20 · arxiv updated 2013/02/22

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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