Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees

Fuente: arXiv
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Autores principales: Budzinski, Thomas, Sénizergues, Delphin
Formato: Preprint
Publicado: 2023
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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