Some remarks on biased recursive trees
Probability
2018-01-16 v1 Combinatorics
Abstract
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform permutations, biased riffle shuffles. The statistics that are treated include the number of nodes with a given number of descendants, the depth of the tree, and the number of branches. The model yields the uniform recursive trees as a certain limit, some new results for the uniform case are obtained as well.
Keywords
Cite
@article{arxiv.1801.04617,
title = {Some remarks on biased recursive trees},
author = {Ella Hiesmayr and Ümit Işlak},
journal= {arXiv preprint arXiv:1801.04617},
year = {2018}
}
Comments
27 pages, partially based on Hiesmayr's master's thesis