Note on a partition limit theorem for rank and crank
Combinatorics
2014-02-26 v1 Probability
Abstract
If L is a partition of n, the rank of L is the size of the largest part minus the number of parts. Under the uniform distribution on partitions, Bringmann, Mahlburg, and Rhoades showed that the rank statistic has a limiting distribution. We identify the limit as the difference between two independent extreme value distributions and as the distribution of B(T) where B(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.
Keywords
Cite
@article{arxiv.1205.1252,
title = {Note on a partition limit theorem for rank and crank},
author = {Persi Diaconis and Svante Janson and Robert C. Rhoades},
journal= {arXiv preprint arXiv:1205.1252},
year = {2014}
}
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3 pages