An analogue of Feller’s theorem for logarithmic combinatorial assemblies

Abstract

We continue our investigations on iterated logarithm laws for additive functions defined on random combinatorial structures called assemblies or abelian partitional structures. Exploiting Feller’s theorem, we obtain sharp upper bounds for a sequence of truncated additive functions. The results imply bounds for the sequence of sizes of components. The main ideas originated from the first author’s number-theoretical papers.