Large deviation principles for abelian monoids
Number Theory
2025-07-01 v2 Probability
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.
Keywords
Cite
@article{arxiv.2506.16970,
title = {Large deviation principles for abelian monoids},
author = {Daniel Keliher and Sun Woo Park},
journal= {arXiv preprint arXiv:2506.16970},
year = {2025}
}
Comments
V2. 10 pages. Made correction to Lemma 3.4 and fixed typos