Large deviation principles for abelian monoids

TL;DR

This paper establishes a large deviation principle for integer-valued additive functions on abelian monoids, extending previous work and deriving a generalized Erdős-Kac theorem as a corollary.

Contribution

It introduces a broad class of large deviation principles for additive functions on abelian monoids, generalizing existing results and connecting to number theory.

Findings

Large deviation principle for additive functions on abelian monoids

Generalized Erdős-Kac theorem derived as a corollary

Extension of previous probabilistic number theory results

Abstract

Following work of Mehrdad and Zhu and of Liu, we prove a large deviation principle for a broad class of integer-valued additive functions defined over abelian monoids. As a corollary, we obtain a large deviation principle for a generalized form of the Erd\H{o}s-Kac theorem due to Liu.