Abstract

I will present connections between modified log-Sobolev inequalities and Poincare inequalities for the p-th moments in which the Euclidean norm of the gradient is replaced by a certain Orlicz type norm related to the energy form in the log-Sobolev inequality. In special cases, using estimates of moments of linear combinations of independent random variables with log-concave tails due to Gluskin and Kwapien, this Poincare inequality can be rewritten in terms of moments of auxiliary independent random variables which allows to obtain a weak decoupling principle for functions with bounded derivatives of higher order, relating their moments to moments of tetrahedral polynomials in independent random variables. In the case of the classical log-Sobolev inequality this leads to an extension of Latala’s inequalities for Gaussian chaos to more general non-Lipschitz functions and non-product measures. If time permits I will also discuss counterparts of such inequalities for polynomials in arbitrary independent subgaussian random variables (to which concentration inequalities for general smooth functions do not apply). Joint work with Witold Bednorz and Pawel Wolff.