RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 4, Pages 696–700 (Mi tvp669)  

This article is cited in 3 scientific papers (total in 3 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.

Full text: PDF file (360 kB)

English version:
Theory of Probability and its Applications, 1966, 11:4, 614–619

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{Sev66}
\by B.~A.~Sevast'yanov
\paper Limit theorems in a scheme of disposal of particles in cells
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 4
\pages 696--700
\mathnet{http://mi.mathnet.ru/tvp669}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=203784}
\zmath{https://zbmath.org/?q=an:0171.39402}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 4
\pages 614--619
\crossref{https://doi.org/10.1137/1111067}


Linking options:
  • http://mi.mathnet.ru/eng/tvp669
  • http://mi.mathnet.ru/eng/tvp/v11/i4/p696

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath  isi
    2. V. G. Mikhailov, “Asymptotic normality in a scheme of finitely dependent distribution of particles in cells”, Math. USSR-Sb., 47:2 (1984), 499–512  mathnet  crossref  mathscinet  zmath
    3. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:260
    Full text:110
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020