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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité