Atypical Decay Rates for Atypical Heights in Random Recursive Trees
Probability
2026-04-23 v1
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 -fold iterated logarithm.
Keywords
Cite
@article{arxiv.2604.20139,
title = {Atypical Decay Rates for Atypical Heights in Random Recursive Trees},
author = {Xinxin Chen and Heng Ma},
journal= {arXiv preprint arXiv:2604.20139},
year = {2026}
}
Comments
19 pages, 3 figures; comments are welcome!