Geodesic
Inequalities and limit theorems for random allocations
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 65 (2011) no. 1

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Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.
Keywords: Random allocation, moment inequality, merge theorem, almost sure limit theorem 
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Fazekas, Istvan; Chuprunov, Alexey; Turi, Jozsef. Inequalities and limit theorems for random allocations. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 65 (2011) no. 1. http://geodesic.mathdoc.fr/item/AUM_2011_65_1_a2/

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