ON WEIGHTED PATH LENGTHS AND DISTANCES IN INCREASING TREES
Markus Kuba, Alois Panholzer · Probability in the Engineering and Informational Sciences · 2007
We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-oriented recursive trees, and binary increasing trees), we can determine the limiting distribution that can be characterized as a generalized Dickman's infinitely divisible distribution.