A random recursive tree model with doubling events

Jakob E. Björnberg and Cécile Mailler

Stochastic Processes and their Applications, 2026, vol. 192, issue C

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.

Keywords: Random tree; Random recursive tree (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104790

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