Concentration functions and entropy bounds for discrete log-concave distributions

TL;DR

This paper investigates bounds on concentration functions and R'enyi entropies for discrete log-concave distributions, leading to new variants of entropy power inequalities.

Contribution

It introduces novel bounds for concentration and entropy measures specifically for discrete log-concave distributions, enhancing understanding of their probabilistic properties.

Findings

Derived new bounds for concentration functions.

Established variants of entropy power inequalities.

Enhanced theoretical understanding of discrete log-concave distributions.

Abstract

Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.