On binary search tree recursions with monomials as toll functions

摘要

We consider distributional recursions which appear in the study of random binary search trees with monomials as toll functions. This extends classical parameters as the internal path length in binary search trees. As our main results we derive asymptotic expansions for the moments of the random variables under consideration as well as limit laws and properties of the densities of the limit distributions. The analysis is based on the contraction method.