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Pré-Publication, Document De Travail Année : 2023

Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees

Résumé

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 $(1-\varepsilon)$-H\"older homeomorphism between two independent copies of the Brownian tree.
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hal-04112383 , version 1 (31-05-2023)

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Thomas Budzinski, Delphin Sénizergues. Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees. 2023. ⟨hal-04112383⟩
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