Majorization and Rényi entropy inequalities via Sperner theory

A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new Rényi entropy inequalities for sums of independent, integer-valued random variables.

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Bibliographic Details
Published in:Discrete mathematics 2019-10, Vol.342 (10), p.2911-2923
Main Authors: Madiman, Mokshay, Wang, Liyao, Woo, Jae Oh
Format: Article
Language:English
Subjects:
Entropy power inequality
Majorization
Posets
Strong Sperner property
Sumset inequality
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Description
Summary:A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new Rényi entropy inequalities for sums of independent, integer-valued random variables.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.03.002