This article is cited in 2 papers

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

A. M. Zubkov^a, O. K. Shibanov<sup>b

a</sup> 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.

UDC: 519.21

Received: 12.08.2008

DOI: 10.4213/mzm6635

 English version: Mathematical Notes, 2009, 85:3, 366–373

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