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A note on the deficit of the logarithmic Sobolev inequality

Volume 45 / 2018

Stephen G. Walker Applicationes Mathematicae 45 (2018), 199-205 MSC: Primary 26D10; Secondary 39B72. DOI: 10.4064/am2360-6-2018 Published online: 24 July 2018


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.


  • Stephen G. WalkerDepartment of Mathematics
    University of Texas at Austin
    Austin, TX 78712, U.S.A.

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