An analogue of Feller's theorem for logarithmic combinatorial assemblies (Q736133)

The authors investigate iterated logarithm laws for additive functions defined on random combinatorial structures called assemblies or abelian partitional structures. Assemblies with logarithmic condition and a quite wide set of additive functions are examined. Exploiting the classical Feller theorem authors obtain a sharp upper bounds for a sequence of truncated additive functions. The main results are applied to derive the sharp bounds for the sequence of sizes of components.