Entropy Inequalities for Sums in Prime Cyclic Groups
Combinatorics
2021-10-20 v4 Information Theory
math.IT
Number Theory
Probability
Abstract
Lower bounds for the R\'enyi 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.
Cite
@article{arxiv.1710.00812,
title = {Entropy Inequalities for Sums in Prime Cyclic Groups},
author = {Mokshay Madiman and Liyao Wang and Jae Oh Woo},
journal= {arXiv preprint arXiv:1710.00812},
year = {2021}
}
Comments
25 pages