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.

32 pages. v2: Several minor edits + Section X added

References in corpus (4)

• Rényi Divergence and Kullback-Leibler Divergence
• The concavity of Rènyi entropy power
• On the problem of reversibility of the entropy power inequality
• Dimensional behaviour of entropy and information

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