Stephen Graham Walker
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
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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
Key concepts: Mathematics, Logarithm, Inequality, Rearrangement inequality, Sobolev inequality, Kantorovich inequality, Poincaré inequality, Cauchy–Schwarz inequality