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Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 3, Pages 599–609 (Mi tvp5241)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Random mappings with component sizes from a given set

A. N. Timashev

Institute of Cryptography, Communications and Informatics, Academy of Federal Security Service of Russian Federation, Moscow

Abstract: The paper is concerned with single-valued mappings from the set of $n$ labeled elements into itself such that the sizes of connected components of the graph corresponding to each mapping lie in a given countable set of positive integers. We find the asymptotic behavior for the number of all such mappings as $n\to\nobreak \infty$. As a conjecture, we formulate sufficient conditions for the convergence of the distribution of the number of components in a random equiprobable mapping of the above form to the normal law (in the local setting). We consider particular cases where this conjecture applies and derive corollaries from it. Conditions are given for the convergence of the distribution of the number of components of a given size to a Poisson distribution law.

Keywords: random mappings, components, saddle-point method, power series, Poisson distribution, asymptotic density.

DOI: https://doi.org/10.4213/tvp5241

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English version:
Theory of Probability and its Applications, 2019, 64:3, 481–489

Bibliographic databases:

Received: 17.11.2017
Revised: 06.03.2018
Accepted:15.03.2018

Citation: A. N. Timashev, “Random mappings with component sizes from a given set”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 599–609; Theory Probab. Appl., 64:3 (2019), 481–489

Citation in format AMSBIB
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\by A.~N.~Timashev
\paper Random mappings with component sizes from a given set
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 3
\pages 599--609
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\jour Theory Probab. Appl.
\yr 2019
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\pages 481--489
\crossref{https://doi.org/10.1137/S0040585X97T989647}
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  • http://mi.mathnet.ru/eng/tvp5241
  • https://doi.org/10.4213/tvp5241
  • http://mi.mathnet.ru/eng/tvp/v64/i3/p599

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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. L. Yakymiv, “Size distribution of the largest component of a random $A$-mapping”, Discrete Math. Appl., 31:2 (2021), 145–153  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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