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  • 1 Institute of Economics, Management and Laws Zatzeva 17, Kazan, Russia Zatzeva 17, Kazan, Russia
  • 2 Institute of Informatics, University of Debrecen P.O. Box 12, 4010 Debrecen, Hungary P.O. Box 12, 4010 Debrecen, Hungary
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Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations. Functional limit theorems for such random processes are obtained.