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Beyond the entropy power inequality, via rearrangements (1307.6018v2)
Published 23 Jul 2013 in cs.IT, math.FA, math.IT, and math.PR
Abstract: A lower bound on the R\'enyi 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 L\'evy processes.