Séminaires : Séminaire d'Analyse Fonctionnelle

Two popular ways of quantifying measure concentration is through the sharp constants that appear in Poincar\'e and log-Sobolev inequalities. In addition to concentration implications, these constants quantify distance to Gaussianity in a strong sense.  In this talk, I'll show how these constants satisfy a certain central limit theorem.  Namely, under repeated convolutions, the Poincar\'e constant of the convolution measure approaches that of the Gaussian measure with the same second moments.  The same is shown for the log-Sobolev constant, under mild regularity assumptions.