Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities
Radosław Adamczak, Dominik Kutek, Michał Strzelecki
Abstract
We prove results about stability under mixtures for transport--entropy inequalities and restricted functional inequalities of Poincaré and log-Sobolev type. We treat Talagrand inequalities of type T2 and T1 together with their generalizations, as well as weak transportation inequalities introduced by Gozlan et al. Our main results provide mild sufficient conditions under which a given inequality may be transferred from mixture components to the mixture itself.
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