The degree profile of random Pólya trees

https://doi.org/10.1016/j.jcta.2012.04.007Get rights and content
Under a Creative Commons license
open access

Abstract

We investigate the profile of random Pólya trees of size n when only nodes of degree d are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process converges weakly to a Brownian excursion local time. Moreover, we investigate the joint distribution of the number of nodes of degrees d1 and d2 on the same level of the tree.

Keywords

Unlabelled trees
Profile
Nodes of fixed degree
Brownian excursion
Local time

Cited by (0)

This research has been supported by FWF (Austrian Science Foundation), National Research Network S9600, grant S9604.