Some central limit theorems for critical beta-splitting tree
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911221022720000 |
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| author | Iksanov, Alexander Nikitin, Anatolii Yakymiv, Roman |
| author_facet | Iksanov, Alexander Nikitin, Anatolii Yakymiv, Roman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some central limit theorems for critical beta-splitting tree Iksanov, Alexander Nikitin, Anatolii Yakymiv, Roman Probability 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. |
| title | Some central limit theorems for critical beta-splitting tree |
| topic | Probability |
| url | https://arxiv.org/abs/2510.17343 |