Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929236592295936 |
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| author | Budzinski, Thomas Sénizergues, Delphin |
| author_facet | Budzinski, Thomas Sénizergues, Delphin |
| contents | We prove that the size of the largest common subtree between two uniform, independent, leaf-labelled random binary trees of size $n$ is typically less than $n^{1/2-\varepsilon}$ for some $\varepsilon>0$. Our proof relies on the coupling between discrete random trees and the Brownian tree and on a recursive decomposition of the Brownian tree due to Aldous. Along the way, we also show that almost surely, there is no $(1-\varepsilon)$-Hölder homeomorphism between two independent copies of the Brownian tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees Budzinski, Thomas Sénizergues, Delphin Probability Combinatorics We prove that the size of the largest common subtree between two uniform, independent, leaf-labelled random binary trees of size $n$ is typically less than $n^{1/2-\varepsilon}$ for some $\varepsilon>0$. Our proof relies on the coupling between discrete random trees and the Brownian tree and on a recursive decomposition of the Brownian tree due to Aldous. Along the way, we also show that almost surely, there is no $(1-\varepsilon)$-Hölder homeomorphism between two independent copies of the Brownian tree. |
| title | Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2304.00905 |