Abstract
We consider weighted path lengths to the extremal leaves in a random
binary search tree. When linearly scaled, the weighted path length to the
minimal label has Dickman's infinitely divisible distribution as a
limit. By contrast, the weighted path length to the maximal label needs to
be centered and scaled to converge to a standard normal variate in
distribution. The exercise shows that path lengths associated with
different ranks exhibit different behaviors depending on the rank.
However, the majority of the ranks have a weighted path length with
average behavior similar to that of the weighted path to the maximal
node.