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On the problem of reversibility of the entropy power inequality

Functional Analysis 2024-05-15 v1 Information Theory math.IT Probability

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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Cite

@article{arxiv.1111.6807,
  title  = {On the problem of reversibility of the entropy power inequality},
  author = {Sergey G. Bobkov and Mokshay M. Madiman},
  journal= {arXiv preprint arXiv:1111.6807},
  year   = {2024}
}

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13 pages