# Entropic CLT for smoothed convolutions and associated entropy bounds

## TL;DR

This paper investigates how the entropy of sums of independent random variables behaves asymptotically when these variables are convolved with a small amount of continuous noise, revealing new entropy bounds.

## Contribution

It introduces an entropic Central Limit Theorem for smoothed convolutions and derives associated entropy bounds, advancing understanding of entropy behavior under noise smoothing.

## Key findings

- Asymptotic entropy behavior characterized for smoothed convolutions
- New entropy bounds established for sums of independent variables
- Enhanced understanding of entropy in noisy convolution scenarios

## Abstract

We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.