This article is cited in 3 scientific papers (total in 3 papers)
Limit theorems in a scheme of disposal of particles in cells
B. A. Sevast'yanov
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.
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Theory of Probability and its Applications, 1966, 11:4, 614–619
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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\paper Limit theorems in a scheme of disposal of particles in cells
\jour Teor. Veroyatnost. i Primenen.
\jour Theory Probab. Appl.
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V. G. Mikhailov, “Convergence to the multidimensional normal law in an equiprobable scheme of distributing particles by groups”, Math. USSR-Sb., 39:2 (1981), 145–167
V. G. Mikhailov, “Asymptotic normality in a scheme of finitely dependent distribution of particles in cells”, Math. USSR-Sb., 47:2 (1984), 499–512
V. G. Mikhailov, “Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications”, Proc. Steklov Inst. Math., 282 (2013), 157–171
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