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Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 4, Pages 696–700
(Mi tvp669)
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This article is cited in 14 scientific papers (total in 14 papers)
Short Communications
Limit theorems in a scheme of disposal of particles in cells
B. A. Sevast'yanov Moscow
Abstract:
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.
Received: 28.12.1965
Citation:
B. A. Sevast'yanov, “Limit theorems in a scheme of disposal of particles in cells”, Teor. Veroyatnost. i Primenen., 11:4 (1966), 696–700; Theory Probab. Appl., 11:4 (1966), 614–619
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