Reversals of R\'enyi Entropy Inequalities under Log-Concavity
Probability
2021-06-01 v1 Information Theory
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
Keywords
Cite
@article{arxiv.2005.10930,
title = {Reversals of R\'enyi Entropy Inequalities under Log-Concavity},
author = {James Melbourne and Tomasz Tkocz},
journal= {arXiv preprint arXiv:2005.10930},
year = {2021}
}