  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.
