"Reversal of Rényi Entropy Inequalities Under Log-Concavity"

We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within $\log e$ of the… Click to show full abstract

We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within $\log e$ of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis, and establish a sharp Rényi version for certain parameters in both the continuous and discrete cases.

Keywords: log concavity; inequalities log; entropy; entropy inequalities; nyi entropy; reversal nyi

Journal Title: IEEE Transactions on Information Theory
Year Published: 2021

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