Some central limit theorems for critical beta-splitting tree

Alexander Iksanov; Anatolii Nikitin; Roman Yakymiv

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arXiv · 2510.17343

Some central limit theorems for critical beta-splitting tree

Alexander Iksanov·Anatolii Nikitin·Roman Yakymiv

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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.

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Alexander Iksanov, Anatolii Nikitin, Roman Yakymiv. 2025-10-20. Some central limit theorems for critical beta-splitting tree. https://arxiv.org/abs/2510.17343

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