Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 97-103
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Yu. V. Bolotnikov. The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells. Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 97-103. http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a11/
@article{MZM_1968_4_1_a11,
author = {Yu. V. Bolotnikov},
title = {The convergence to {a~Gaussian} process of the number of empty cells in the classical problem of distributing particles among cells},
journal = {Matemati\v{c}eskie zametki},
pages = {97--103},
year = {1968},
volume = {4},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a11/}
}
TY - JOUR
AU - Yu. V. Bolotnikov
TI - The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells
JO - Matematičeskie zametki
PY - 1968
SP - 97
EP - 103
VL - 4
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a11/
LA - ru
ID - MZM_1968_4_1_a11
ER -
%0 Journal Article
%A Yu. V. Bolotnikov
%T The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells
%J Matematičeskie zametki
%D 1968
%P 97-103
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a11/
%G ru
%F MZM_1968_4_1_a11
We consider a case in which $n$ particles are distributed independently of one another in $N$ cells. We examine the behavior of the number of empty cells, $\mu_0(n)$, as a random function of the parameter $n$ when $n,N\to\infty$. We prove that for suitable variation of the time parameter, $\mu_0(n)$ will converge to a Gaussian process in the following cases: a) $n/N\to\infty$, $n/N-\ln N\to-\infty$; b) $n/N\to0$, $n^2/N\to\infty$.
