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Remarks on the R\'{e}nyi Entropy of a sum of IID random variables

Information Theory 2019-12-12 v2 math.IT Probability

Abstract

In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the R\'{e}nyi entropy of the sum of independent random variables. Through a variational analysis, we show that the generalized Gaussian fails to be a minimizer for the problem.

Keywords

Cite

@article{arxiv.1904.08038,
  title  = {Remarks on the R\'{e}nyi Entropy of a sum of IID random variables},
  author = {Benjamin Jaye and Galyna V. Livshyts and Grigoris Paouris and Peter Pivovarov},
  journal= {arXiv preprint arXiv:1904.08038},
  year   = {2019}
}

Comments

To appear in IEEE Transactions in Information Theory