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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 223, Pages 227–250
(Mi znsl4389)
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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
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
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
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https://www.mathnet.ru/eng/znsl4389 https://www.mathnet.ru/eng/znsl/v223/p227
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Abstract page: | 135 | Full-text PDF : | 96 |
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