Majorization and Rényi Entropy Inequalities via Sperner Theory

Abstract

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.

Introduction was completely rewritten and there are numerous corrections. Expansion of background on Sperner theory, and several references are added

References in corpus (7)

• Dimensional behaviour of entropy and information
• Rogozin's convolution inequality for locally compact groups
• Combinatorial Entropy Power Inequalities: A Preliminary Study of the Stam region
• Entropy Inequalities for Sums in Prime Cyclic Groups
• Two remarks on generalized entropy power inequalities
• Rigidity of proper colorings of ${\mathbb{Z}}^d$
• An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-Rényi Entropy Power Inequality for Integer Valued Random Variables

Cited by in corpus (12)

• Combinatorial Entropy Power Inequalities: A Preliminary Study of the Stam region
• Entropy Inequalities for Sums in Prime Cyclic Groups
• The Differential Entropy of Mixtures: New Bounds and Applications
• Two remarks on generalized entropy power inequalities
• Bernoulli sums and Rényi entropy inequalities
• Conditional Rényi entropy and the relationships between Rényi capacities
• Volumes of subset Minkowski sums and the Lyusternik region
• Rényi Bounds on Information Combining
• Generalizations of Fano's Inequality for Conditional Information Measures via Majorization Theory
• A Note on Equivalent Conditions for Majorization
• Entropy-variance inequalities for discrete log-concave random variables via degree of freedom
• The norm of the Fourier transform on compact or discrete abelian groups