# Remarks on the R\'{e}nyi Entropy of a sum of IID random variables

## TL;DR

This paper investigates a conjecture regarding the Rényi entropy of sums of IID variables, revealing that the generalized Gaussian distribution does not minimize the entropy as previously conjectured.

## Contribution

The study disproves a conjecture by showing that the generalized Gaussian is not the entropy minimizer for sums of independent variables.

## Key findings

- Generalized Gaussian does not minimize Rényi entropy for sums of IID variables.
- Disproves a conjecture by Madiman and Wang.
- Uses variational analysis to reach conclusions.

## Abstract

In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the R\'{e}nyi entropy of the sum of independent random variables. Through a variational analysis, we show that the generalized Gaussian fails to be a minimizer for the problem.