Hoppe trees, random recursive sets and their barycentre

Mathias Rafler

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arXiv · 1207.1636

Hoppe trees, random recursive sets and their barycentre

Mathias Rafler

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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.

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Mathias Rafler. 2012-07-06. Hoppe trees, random recursive sets and their barycentre. https://arxiv.org/abs/1207.1636

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