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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}
}