English

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

R2 v1 2026-07-01T03:26:34.930Z