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Matematicheskie Zametki, 2009, Volume 85, Issue 3, Pages 373–381
DOI: https://doi.org/10.4213/mzm6635 (Mi mzm6635) 		 
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
Full-text PDF (431 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm6635
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.
Received: 12.08.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 3, Pages 366–373
DOI: https://doi.org/10.1134/S0001434609030079
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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