Entropies of sums of independent gamma random variables

TL;DR

This paper investigates the entropy properties of sums of independent gamma variables, providing new bounds and proofs that extend existing results in the field of information theory and probability.

Contribution

It introduces novel Schur-convexity results and nonasymptotic Rényi entropy bounds for weighted sums of gamma variables, extending prior work with simplified proofs.

Findings

Established Schur-convexity results under fixed variance.

Derived nonasymptotic bounds on Rényi entropies.

Extended and simplified previous entropy bounds for gamma sums.

Abstract

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their R\'enyi entropies. In particular, this pertains to the recent results by Bartczak-Nayar-Zwara as well as Bobkov-Naumov-Ulyanov, offering simple proofs of the former and extending the latter.