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