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PAC

Information Center for Mathematical Science

PAC

NOTE ON A PARTITION LIMIT THEOREM FOR RANK AND CRANK
Author PERSI DIACONIS (Stanford University)
Homepage Url http://www-stat.stanford.edu/~cgates/PERSI/year.html
Coauthors SVANTE JANSON, ROBERT C. RHOADES
Abstract If  is a partition of n, the rank rk() is the size of the largest part minus the number of parts. Under the uniform distribution on partitions, in Bringmann-Mahlburg- Rhoades [4] it is shown that rk()/p6n has a limiting distribution. We identify the limit as the difference between two independent extreme value distributions and as the distribution of (T ) where (t) is standard Brownian motion and T is the first time that an independent three-dimensional Brownian motion hits the unit sphere. The same limit holds for the crank.
Abstract Url http://arxiv.org/pdf/1205.1252v1.pdf