Beyond the Entropy Power Inequality, via Rearrangements

Abstract

A lower bound on the Rényi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of Lévy processes.