A random recursive tree model with doubling events

TL;DR

This paper introduces a novel random tree model with global doubling events, analyzing its growth, degree distribution, and height, revealing complex behaviors due to these global structural changes.

Contribution

The paper presents a new recursive tree model incorporating doubling events and provides asymptotic analysis of its size, degree distribution, and height profile.

Findings

Asymptotic size of the tree at large times

Degree distribution characterized

Lower bound for tree height established

Abstract

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size of this tree at large times, its degree distribution, and its height profile. We also prove a lower bound for its height. Because of the doubling events that affect the tree globally, the proofs are all much more intricate than in the case of the random recursive tree in which the growing operation is always local.