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Note on a partition limit theorem for rank and crank
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 45, no 3, 551-553 p.Article in journal (Refereed) Published
Abstract [en]

If lambda is a partition of n, then the rank rk(lambda) is the size of the largest part minus the number of parts. Under the uniform distribution on partitions, in K. Bringmann, K. Mahlburg, and R. C. Rhoades (Bull. Lond. Math. Soc., 43 (2011) 661-672), it is shown that <inline-graphic xlink:href="BDS121IM1" xmlns:xlink="http://www.w3.org/1999/xlink"/> has a limiting distribution. We identify the limit as the difference between two independent extreme value distributions and as the distribution of beta(T), where beta(t) is standard Brownian motion and T is the first time that an independendent 3-dimensional Brownian motion hits the unit sphere. The same limit holds for the crank.

Place, publisher, year, edition, pages
2013. Vol. 45, no 3, 551-553 p.
National Category
Natural Sciences
URN: urn:nbn:se:uu:diva-202353DOI: 10.1112/blms/bds121ISI: 000318803500010OAI: oai:DiVA.org:uu-202353DiVA: diva2:632016
Available from: 2013-06-24 Created: 2013-06-24 Last updated: 2013-06-24Bibliographically approved

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Janson, Svante
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