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 
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/
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     author = {A. M. Zubkov and O. K. Shibanov},
     title = {A {Poisson} limit theorem for a two-stage equiprobable scheme of allocating particles into cells},
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     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_4_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1976

[2] Zubkov A. M., Shibanov O. K., “Mnogostupenchatye skhemy razmescheniya chastits po yacheikam”, Obozrenie prikladnoi i promyshlennoi matematiki, 9:1 (2002), 115–116 | MR

[3] Zubkov A. M., Shibanov O. K., “Dvukhstupenchataya skhema razmescheniya chastits po yacheikam”, Obozrenie prikladnoi i promyshlennoi matematiki, 9:2 (2002), 378–379