Atypical Decay Rates for Atypical Heights in Random Recursive Trees

Xinxin Chen; Heng Ma

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arXiv · 2604.20139

Atypical Decay Rates for Atypical Heights in Random Recursive Trees

Xinxin Chen·Heng Ma

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Abstract

We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows to infinity more slowly than any $n$-fold iterated logarithm.

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Xinxin Chen, Heng Ma. 2026-04-22. Atypical Decay Rates for Atypical Heights in Random Recursive Trees. https://arxiv.org/abs/2604.20139

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