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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 223, Pages 227–250 (Mi znsl4389)  
This article is cited in 4 scientific papers (total in 4 papers)

Combinatorial and algorithmic methods

Asymptotics of random partitions of a set

Yu. V. Yakubovich

Saint-Petersburg State University
Full-text PDF (1073 kB) Citations (4)
Abstract: This paper contains two results on the asymptotic behavior of uniform probability measure on partitions of a finite set as its cardinality tends to infinity. The first one states that there exists a normalization of the corresponding Young diagrams such that the induced measure has a weak limit. This limit is shown to be a $\delta$-measure supported by the unit square (Theorem 1). It implies that the majority of partition blocks have approximately the same length. Theorem 2 clarifies the limit distribution of these blocks.
The techniques used can also be useful for deriving a range of analogous results. Bibliography: 13 titles.
Received: 15.01.1995
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 6, Pages 4124–4137
DOI: https://doi.org/10.1007/BF02355807
Bibliographic databases:
Document Type: Article
UDC: 519.217
Language: Russian
Citation: Yu. V. Yakubovich, “Asymptotics of random partitions of a set”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Zap. Nauchn. Sem. POMI, 223, POMI, St. Petersburg, 1995, 227–250; J. Math. Sci. (New York), 87:6 (1997), 4124–4137
Citation in format AMSBIB
\Bibitem{Yak95}
\by Yu.~V.~Yakubovich
\paper Asymptotics of random partitions of a~set
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~I
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 223
\pages 227--250
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4389}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1374322}
\zmath{https://zbmath.org/?q=an:0909.60017|0887.60017}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 6
\pages 4124--4137
\crossref{https://doi.org/10.1007/BF02355807}
Linking options:
  • https://www.mathnet.ru/eng/znsl4389
  • https://www.mathnet.ru/eng/znsl/v223/p227
    • This publication is cited in the following 4 articles:
    1. Ross J. Kang, Colin McDiarmid, Bruce Reed, Alex Scott, “For most graphs H, most H‐free graphs have a linear homogeneous set”, Random Struct Algorithms, 45:3 (2014), 343  crossref
    2. Michael M. Erlihson, Boris L. Granovsky, “Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case”, Ann. Inst. H. Poincaré Probab. Statist., 44:5 (2008)  crossref
    3. A. M. Vershik, G. A. Freiman, Yu. V. Yakubovich, “A local limit theorem for random strict partitions”, Theory Probab. Appl., 44:3 (2000), 453–468  mathnet  mathnet  crossref  crossref  isi
    4. A. M. Vershik, “Statistical Mechanics of Combinatorial Partitions, and Their Limit Shapes”, Funct. Anal. Appl., 30:2 (1996), 90–105  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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