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Mat. Sb. (N.S.), 1976, Volume 99(141), Number 1, Pages 121–133 (Mi msb2742)  

This article is cited in 15 scientific papers (total in 15 papers)

Asymptotic normality of some variables connected with the cyclic structure of random permutations

Yu. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov


Abstract: Asymptotic normality as $n\to\infty$ is proved for certain random variables connected with the cyclic structure of a random permutation of degree $n$, under a nonuniform probability distribution on the set of all permutations, in particular, the asymptotic normality of the number of all cycles.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 28:1, 107–117

Bibliographic databases:

Document Type: Article
UDC: 519.21
MSC: Primary 60E05, 60F05; Secondary 62E20
Received: 03.06.1975

Citation: Yu. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov, “Asymptotic normality of some variables connected with the cyclic structure of random permutations”, Mat. Sb. (N.S.), 99(141):1 (1976), 121–133; Math. USSR-Sb., 28:1 (1976), 107–117

Citation in format AMSBIB
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\by Yu.~V.~Bolotnikov, V.~N.~Sachkov, V.~E.~Tarakanov
\paper Asymptotic normality of some variables connected with the cyclic structure of random permutations
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 1
\pages 121--133
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=415713}
\zmath{https://zbmath.org/?q=an:0335.60005}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 1
\pages 107--117
\crossref{https://doi.org/10.1070/SM1976v028n01ABEH001642}
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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. V. Bolotnikov, V. N. Sachkov, V. E. Tarakanov, “On some classes of random variables on cycles of permutations”, Math. USSR-Sb., 36:1 (1980), 87–99  mathnet  crossref  mathscinet  zmath  isi
    2. Lyuben R. Mutafchiev, “Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures”, Random Struct Alg, 3:4 (1992), 403  crossref  mathscinet  zmath
    3. A. N. Timashev, “On the distribution of the number of cycles of a given length in the class of permutations with known number of cycles”, Discrete Math. Appl., 11:5 (2001), 471–483  mathnet  crossref  mathscinet  zmath
    4. A. L. Yakymiv, “On the distribution of the $m$th maximal cycle lengths of random $A$-permutations”, Discrete Math. Appl., 15:5 (2005), 527–546  mathnet  crossref  crossref  mathscinet  zmath  elib
    5. A. L. Yakymiv, “Limit theorem for the general number of cycles in a random $A$-permutation”, Theory Probab. Appl., 52:1 (2008), 133–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. A. L. Yakymiv, “Random $A$-Permutations: Convergence to a Poisson Process”, Math. Notes, 81:6 (2007), 840–846  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. A. L. Yakymiv, “On the Number of $A$-Mappings”, Math. Notes, 86:1 (2009), 132–139  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. L. Yakymiv, “Limit Theorem for the Middle Members of Ordered Cycle Lengths in Random $A$-Permutations”, Theory Probab. Appl., 54:1 (2010), 114–128  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. L. Yakymiv, “A limit theorem for the logarithm of the order of a random $A$-permutation”, Discrete Math. Appl., 20:3 (2010), 247–275  mathnet  crossref  crossref  mathscinet  zmath  elib  elib
    10. A. L. Yakymiv, “Asymptotics of the Moments of the Number of Cycles of a Random $A$-Permutation”, Math. Notes, 88:5 (2010), 759–766  mathnet  crossref  crossref  mathscinet  isi
    11. A. L. Yakymiv, “Random $A$-permutations and Brownian motion”, Proc. Steklov Inst. Math., 282 (2013), 298–318  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. A. L. Yakymiv, “On the number of cyclic points of random $A$-mapping”, Discrete Math. Appl., 23:5-6 (2013), 503–515  mathnet  crossref  crossref  mathscinet  elib  elib
    13. A. L. Yakymiv, “On a number of components in a random $A$-mapping”, Theory Probab. Appl., 59:1 (2015), 114–127  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    14. A. L. Yakymiv, “On the Number of Components of Fixed Size in a Random $A$-Mapping”, Math. Notes, 97:3 (2015), 468–475  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. L. Yakymiv, “Limit theorems for the logarithm of the order of a random $A$-mapping”, Discrete Math. Appl., 27:5 (2017), 325–338  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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