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A quantitative log-Sobolev inequality for a two parameter family of functions (1302.4910v1)
Published 20 Feb 2013 in math.AP, math.OC, and math.PR
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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