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Teor. Veroyatnost. i Primenen., 1969, Volume 14, Issue 1, Pages 64–77 (Mi tvp1117)  

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

On the distribution of the number of vertices in strata of a random tree

V. E. Stepanov

Moscow

Abstract: The set of trees with $m+1$ distinguishable vertices one of which is taken as a root is considered. In every tree all the vertices are distributed in strata with respect to the root according to the lengths of paths which connect them to the root.
Let $\zeta_{m,j}$ be the number of vertices in the $j$-th stratum of a tree chosen at random.
We prove that if $m$ and $j\to\infty$ so that $j/\sqrt m\to\alpha$, $0<\alpha_1\le\alpha<\alpha_2<\infty$, then the distributions of random variables $\zeta_{m,j}/\sqrt m$ converge to a limit distribution. Explicit expressions for moments and the density of the limit distribution are found.

Full text: PDF file (825 kB)

English version:
Theory of Probability and its Applications, 1969, 14:1, 65–78

Bibliographic databases:

Received: 05.11.1967

Citation: V. E. Stepanov, “On the distribution of the number of vertices in strata of a random tree”, Teor. Veroyatnost. i Primenen., 14:1 (1969), 64–77; Theory Probab. Appl., 14:1 (1969), 65–78

Citation in format AMSBIB
\Bibitem{Ste69}
\by V.~E.~Stepanov
\paper On the distribution of the number of vertices in strata of a~random tree
\jour Teor. Veroyatnost. i Primenen.
\yr 1969
\vol 14
\issue 1
\pages 64--77
\mathnet{http://mi.mathnet.ru/tvp1117}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=246344}
\zmath{https://zbmath.org/?q=an:0196.21001|0172.21902}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 1
\pages 65--78
\crossref{https://doi.org/10.1137/1114007}


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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. Yu. L. Pavlov, “Limit theorems for the number of trees of a given size in a random forest”, Math. USSR-Sb., 32:3 (1977), 335–345  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. A. A. Serov, “Images of a finite set under iterations of two random dependent mappings”, Discrete Math. Appl., 26:3 (2016), 175–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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