English

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

R2 v1 2026-06-22T23:44:50.457Z