Remarks on the Rényi Entropy of a sum of IID random variables

2019/04/17 by Jaye, Benjamin, Livshyts, Galyna V., Paouris, Grigoris +1
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.1904.08038

Abstract

In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the Rényi 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.

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