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Reversals of Rényi Entropy Inequalities under Log-Concavity (2005.10930v1)
Published 21 May 2020 in math.PR, cs.IT, and math.IT
Abstract: We establish a discrete analog of the R\'enyi 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 R\'enyi version for certain parameters in both the continuous and discrete cases