Work

Entropy Inequalities for Sums in Prime Cyclic Groups

Year: 2021

Type: article

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 [ Duke Math. J., 107 (2001), pp. 239--263] 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.

Source: SIAM Journal on Discrete Mathematics

DOI: 10.1137/18m1185570

Authors: Mokshay Madiman, Liyao Wang, Jae Oh Woo

Institutions: University of Delaware, Yale University

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CIF: Medium: Collaborative Research: Information Theory and Statistical Inference from Large-Alphabet Data, CAREER: An integrated probabilistic approach to discrete and continuous extremal problems via information theory, G6671297155