Hoppe trees, random recursive sets and their barycentre

TL;DR

This paper studies the asymptotic behavior of the barycenter of a recursively constructed random set of points, using Hoppe trees to analyze the joint distribution of total length and Wiener index.

Contribution

It introduces a new recursive model for random point sets and derives a limit theorem for Hoppe trees' total length and Wiener index.

Findings

Limit theorem for Hoppe trees' total length and Wiener index

Asymptotic behavior of the barycenter of the random set

New recursive construction model for random point sets

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.