Entropy Inequalities for Sums in Prime Cyclic Groups

Abstract

Lower bounds for the Rényi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in prime cyclic groups building on Lev (2001), and notions of stochastic ordering. Several applications are developed, including to discrete entropy power inequalities, the Littlewood-Offord problem, and counting solutions of certain linear systems.

25 pages

References in corpus (2)

• Combinatorial Entropy Power Inequalities: A Preliminary Study of the Stam region
• Majorization and Rényi Entropy Inequalities via Sperner Theory

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