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

04/17/2019

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by   Benjamin Jaye, et al.

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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.