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
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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) $n/N\to0$, $n^2/N\to\infty$.
@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},
publisher = {mathdoc},
volume = {4},
number = {1},
year = {1968},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a11/ %G ru %F MZM_1968_4_1_a11
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/