The probability of successful allocation of particles in cells (the general case)
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 119-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $p_{nN}$ be the probability of successful allocation of $n$ groups of particles in $N$ cells with the following assumptions: (a) each group contains $m$ particles and has allocation as a general allocation scheme; (b) each cell contains at most $r$ particles from the same group; (c) events connected with different groups are independent. We obtain an asymptotically exact bound of $p_{nN}$ as $n,N\to\infty$ such that $n/N$ is bounded. Applications to problems in error-correcting coding are considered.
@article{FPM_2013_18_5_a5,
     author = {I. R. Kayumov and A. N. Chuprunov},
     title = {The probability of successful allocation of particles in cells (the general case)},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {119--128},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a5/}
}
TY  - JOUR
AU  - I. R. Kayumov
AU  - A. N. Chuprunov
TI  - The probability of successful allocation of particles in cells (the general case)
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 119
EP  - 128
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a5/
LA  - ru
ID  - FPM_2013_18_5_a5
ER  - 
%0 Journal Article
%A I. R. Kayumov
%A A. N. Chuprunov
%T The probability of successful allocation of particles in cells (the general case)
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 119-128
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a5/
%G ru
%F FPM_2013_18_5_a5
I. R. Kayumov; A. N. Chuprunov. The probability of successful allocation of particles in cells (the general case). Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 119-128. http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a5/

[1] Avkhadiev F. G., Kayumov I. R., Chuprunov A. N., “Issledovanie veroyatnosti uspeshnogo razmescheniya chastits po yacheikam metodami kompleksnogo analiza”, Tr. Mat. tsentra im. N. I. Lobachevskogo, 19, 2003, 6–7 | MR

[2] Kolchin V. F., Sluchainye grafy, Fizmatlit, M., 2000 | MR | Zbl

[3] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, M., 1976 | MR | Zbl

[4] Novikov F. A., Diskretnaya matematika dlya programmistov, Piter, 2004

[5] Timashev A. N., Asimptoticheskie razlozheniya v veroyatnostnoi kombinatorike, TVP, M., 2011

[6] Timashev A. N., Bolshie ukloneniya v veroyatnostnoi kombinatorike, Akademiya, M., 2011

[7] Timashev A. N., Obobschënnaya skhema razmescheniya v zadachakh veroyatnostnoi kombinatoriki, Akademiya, M., 2011

[8] Chuprunov A. N., Khamdeev B. I., “O veroyatnosti ispravleniya oshibok pri pomekhoustoichivom kodirovanii, kogda chislo oshibok prinadlezhit nekotoromu konechnomu mnozhestvu”, Inform. i eë primen., 3:3 (2009), 52–59

[9] Chuprunov A. N., Khamdeev B. I., “O veroyatnosti ispravleniya oshibok pri pomekhoustoichivom kodirovanii, esli chislo oshibok sluchaino”, Diskret. mat., 22:2 (2010), 41–50 | DOI | MR | Zbl

[10] Chuprunov A. N., Khamdeev B. I., “O veroyatnosti ispravleniya oshibok pri pomekhoustoichivom kodirovanii, kogda chislo oshibok sluchainoe mnozhestvo”, Izv. vyssh. uchebn. zaved. Matematika, 2010, no. 8, 81–88 | MR | Zbl

[11] Avkhadiev F. G., Chuprunov A. N., “The probability of a successful allocation of ball groups by boxes”, Lobachevskii J. Math., 25 (2007), 3–7 | MR | Zbl