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On the problem of reversibility of the entropy power inequality
Published 29 Nov 2011 in math.FA, cs.IT, math.IT, and math.PR | (1111.6807v1)
Abstract: As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.
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