Geodesic
Limit theorems for allocation of particles over different cells with restrictions
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 712-725 Cet article a éte moissonné depuis la source Math-Net.Ru

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Equiprobable allocation schemes of $n$ indistinguishable or distinguishable particles over $N$ distinguishable cells are considered provided the fillings of the cells take on values in a fixed subset $A$ of the set of nonnegative integers. Local normal and Poisson theorems are proved for the distributions of the number of cells, each of which contains exactly $r$ particles, and for the number of cycles of length $r\in A$ in a permutation selected at random and equiprobable from the set of all permutations of order $n$ with $N$ cycles $(N\le n)$ whose lengths are elements of a set $A\subsetN$. It is assumed that $n,N\to\infty$ in the central domain.
Keywords: random allocations, asymptotic expansions, saddle-point method, local normal theorem. 
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     author = {A. N. Timashev},
     title = {Limit theorems for allocation of particles over different cells with restrictions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2004},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a4/}
}
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A. N. Timashev. Limit theorems for allocation of particles over different cells with restrictions. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 712-725. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a4/

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