An analogue of Feller's theorem for logarithmic combinatorial assemblies |
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| Authors: | E. Manstavičius J. Norkūnienė |
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| Affiliation: | (1) Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania;(2) Department of Mathematical Statistics, Vilnius Gediminas Technical University, Saulėetekio av. 11, LT-10223 Vilnius, Lithuania |
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| 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. |
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| Keywords: | random combinatorial structure component size law of iterated logarithm upper class lower class |
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