Geodesic
A Poisson limit theorem for a two-stage equiprobable scheme of allocating particles into cells
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 99-104

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We consider a two-stage scheme of allocating particles into cells. At the first stage, $N_0$ initial particles are independently and equiprobably allocated into $N_1$ cells of the first layer. At the second stage, these $N_1$ cells are taken as particles which are independently and equiprobably allocated into $N_2$ cells of the second layer. We present conditions under which the distribution of the number of cells of the second layer containing exactly $r$ particles converges to the Poisson law. 
@article{DM_2006_18_4_a8,
     author = {A. M. Zubkov and O. K. Shibanov},
     title = {A {Poisson} limit theorem for a two-stage equiprobable scheme of allocating particles into cells},
     journal = {Diskretnaya Matematika},
     pages = {99--104},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_4_a8/}
}
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A. M. Zubkov; O. K. Shibanov. A Poisson limit theorem for a two-stage equiprobable scheme of allocating particles into cells. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 99-104. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a8/