Geodesic
Asymptotics of random partitions of a set
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 227-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Yu. V. Yakubovich},
     title = {Asymptotics of random partitions of a~set},
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Yu. V. Yakubovich. Asymptotics of random partitions of a set. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 227-250. http://geodesic.mathdoc.fr/item/ZNSL_1995_223_a12/