Hoppe trees, random recursive sets and their barycentre

Mathias Rafler

Hoppe trees, random recursive sets and their barycentre

Probability 2012-07-09 v1

Authors: Mathias Rafler

Abstract

We consider a recursively defined random set of points and its barycenter, where the random set is constructed by the following inductive rule: Given a realization of $n-1$ points, one of them is picked at random and serves as a source the $n$ -th point. We discuss the asymptotic behaviour of the barycentre of this random set. The main analysis relies on the analsis of Hoppe trees, for which we derive a limit theorem for the joint distribution of total length and Wiener index.

Keywords

random trees phylogenetic trees trees

Cite

@article{arxiv.1207.1636,
  title  = {Hoppe trees, random recursive sets and their barycentre},
  author = {Mathias Rafler},
  journal= {arXiv preprint arXiv:1207.1636},
  year   = {2012}
}

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