Some central limit theorems for critical beta-splitting tree
Probability
2025-10-21 v1
Abstract
We further explore a connection initially unveiled in Iksanov (2025) between critical beta-splitting trees and infinite `balls-in-boxes' schemes. Using the connection, we derive a new joint central limit theorem for components of the height of a leaf chosen uniformly at random in the discrete version of a critical beta-splitting tree. Also, we obtain a joint central limit theorem for the heights in the discrete and continuous versions of a critical beta-splitting tree.
Keywords
Cite
@article{arxiv.2510.17343,
title = {Some central limit theorems for critical beta-splitting tree},
author = {Alexander Iksanov and Anatolii Nikitin and Roman Yakymiv},
journal= {arXiv preprint arXiv:2510.17343},
year = {2025}
}
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submitted for publication