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Mat. Zametki, 2009, Volume 85, Issue 3, Pages 373–381 (Mi mz6635)  

This article is cited in 2 scientific papers (total in 2 papers)

Time Required to Unify All Particles in the Scheme of Equiprobable Allocation into a Sequence of Cell Layers

A. M. Zubkova, O. K. Shibanovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: We study the scheme of equiprobable allocations of particles into a sequence of cell layers, where the particles put into the same cell are considered as a single particle. We present conditions under which, with a positive probability, there exist nonunified particles at each of the layers. For the case in which the number of cells at each of the layers is equal to the number of original particles, we prove the limit theorem for the time instant at which all the particles are unified into a single particle.

Keywords: allocation of particles into cells, limit theorem, Markov chain, random variable, convergence in distribution

DOI: https://doi.org/10.4213/mzm6635

Full text: PDF file (431 kB)
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English version:
Mathematical Notes, 2009, 85:3, 366–373

Bibliographic databases:

UDC: 519.21
Received: 12.08.2008

Citation: A. M. Zubkov, O. K. Shibanov, “Time Required to Unify All Particles in the Scheme of Equiprobable Allocation into a Sequence of Cell Layers”, Mat. Zametki, 85:3 (2009), 373–381; Math. Notes, 85:3 (2009), 366–373

Citation in format AMSBIB
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    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. A. M. Zubkov, A. A. Serov, “Images of subset of finite set under iterations of random mappings”, Discrete Math. Appl., 25:3 (2015), 179–185  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. A. V. Lebedev, “Stochastic operation induced by group allocation of particles and generalized branching processes”, Problems Inform. Transmission, 53:4 (2017), 381–390  mathnet  crossref  isi  elib
  • Математические заметки Mathematical Notes
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