Work

Some central limit theorems for critical beta-splitting tree

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.17343

Authors: Iksanov, Alexander, Nikitin, Anatolii, Yakymiv, Roman

Institutions: Taras Shevchenko National University of Kyiv, Jan Kochanowski University, National University Ostroh Academy

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation of Ukraine, National Research Foundation

Award: G2435284695

OpenAlex ID: W4415901678

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