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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The structure of random partitions of large integers

Author: Bert Fristedt
Journal: Trans. Amer. Math. Soc. 337 (1993), 703-735
MSC: Primary 11K99; Secondary 05A17, 11P82
MathSciNet review: 1094553
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Abstract: Random partitions of integers are treated in the case where all partitions of an integer are assumed to have the same probability. The focus is on limit theorems as the number being partitioned approaches $ \infty $. The limiting probability distribution of the appropriately normalized number of parts of some small size is exponential. The large parts are described by a particular Markov chain. A central limit theorem and a law of large numbers holds for the numbers of intermediate parts of certain sizes. The major tool is a simple construction of random partitions that treats the number being partitioned as a random variable. The same technique is useful when some restriction is placed on partitions, such as the requirement that all parts must be distinct.

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Keywords: Random partitions, integer partitions, probabilistic limit theorems
Article copyright: © Copyright 1993 American Mathematical Society