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Asymptotic results on Hoppe trees and their variations

Part of: Graph theory Combinatorial probability

Published online by Cambridge University Press:  16 July 2020

Ella Hiesmayr  and
Ümit Işlak
Ella Hiesmayr*
Affiliation:
University of California, Berkeley
Ümit Işlak*
Affiliation:
Boğaziçi University
*
*Postal address: University of California, Berkeley, U.S. Email: ella.hiesmayr@berkeley.edu
**Postal address: Boğaziçi University, Istanbul, Turkey. Email: umit.islak1@boun.edu.tr
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Abstract

A uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model more flexible for applications. We analyse the number of leaves, the height, the depth, the number of branches, and the size of the largest branch in these weighted trees.

Keywords

Uniform recursive treesHoppe treesEwens sampling formularandom permutationscouplingrandom tree statistics

MSC classification

Primary: 05C80: Random graphs
Secondary: 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 441 - 457
Copyright
© Applied Probability Trust 2020

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