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Asymptotics of random partitions of a set

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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 δ-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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Authors
  1. Yu. Yakubovich
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 227–250.

The paper is supported by International Science Foundation, grant MQV-100.

Translated by Yu. Yakubovich

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Yakubovich, Y. Asymptotics of random partitions of a set. J Math Sci 87, 4124–4137 (1997). https://doi.org/10.1007/BF02355807

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  • DOI: https://doi.org/10.1007/BF02355807

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