Asymptotic behavior of R\'enyi entropy in the central limit theorem

TL;DR

This paper investigates how Renyi entropy behaves asymptotically in the context of the central limit theorem, focusing on monotonicity properties as the number of summands increases.

Contribution

It provides new insights into the asymptotic behavior and monotonicity of Renyi entropy in the CLT under certain moment conditions.

Findings

Renyi entropy exhibits specific asymptotic patterns in the CLT.

Monotonicity of Renyi entropy is established under certain moment hypotheses.

The results extend understanding of entropy behavior in sum distributions.

Abstract

We explore an asymptotic behavior of R\'enyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.