Large deviation principles for abelian monoids

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 Erdős-Kac theorem due to Liu.

V2. 10 pages. Made correction to Lemma 3.4 and fixed typos