Geodesic
Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 83-93

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A classical scheme of random equiprobable allocations of $n$ particles into $N$ cells is considered. We find an asymptotic formula for the probability that the number of empty cells is equal to $k$ under the condition that $n, N \to \infty$ in such a way that $n/(N - k)$ is bounded and separated from 1 from below.
Keywords: random equiprobable allocations, number of empty cells, local limit theorems. 
@article{DM_2021_33_4_a7,
     author = {O. P. Orlov},
     title = {Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations},
     journal = {Diskretnaya Matematika},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_4_a7/}
}
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O. P. Orlov. Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 83-93. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a7/