The Entropic Erd\H{o}s-Kac Limit Theorem

TL;DR

This paper establishes entropic and total variation forms of the Erd ext{o}s-Kac limit theorem, providing a deeper understanding of the distribution of maximum partial sums of i.i.d. variables with densities.

Contribution

It introduces entropic and total variation versions of the Erd ext{o}s-Kac limit theorem, extending classical results to new probabilistic metrics.

Findings

Proves entropic version of the Erd ext{o}s-Kac limit theorem.

Establishes total variation convergence for maximum partial sums.

Extends classical limit theorems to density-based i.i.d. variables.

Abstract

We prove entropic and total variation versions of the Erd\H{o}s-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.