Limit theorems in a scheme of disposal of particles in cells
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 4, pp. 696-700
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We consider two schemes of disposal of $n$ particles into $N$ cells. In scheme I each particle may fall into any cell with the same probability $1/N$ independently of what happens to the other particles. In scheme II $n$ particles are divided in $n/m$ groups each group containing $m$ particles. The groups are disposed at random into $N$ cells independently of each other all particles of any group being disposed in different cells. Theprobability of any disposal of $m$ particles of each group is equal to $1/С^m_N$. Let $\mu_r(\mu_r')$ be the number of cells containing exactly $r$ particles in scheme I (II). We prove that the limit theorems for $\mu_r$ and $\mu'_r$ as $n$, $N\to\infty$ are the same.
@article{TVP_1966_11_4_a9,
author = {B. A. Sevast'yanov},
title = {Limit theorems in a scheme of disposal of particles in cells},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {696--700},
publisher = {mathdoc},
volume = {11},
number = {4},
year = {1966},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_4_a9/}
}
B. A. Sevast'yanov. Limit theorems in a scheme of disposal of particles in cells. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 4, pp. 696-700. http://geodesic.mathdoc.fr/item/TVP_1966_11_4_a9/