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The continuum random tree is the scaling limit of unlabelled unrooted trees

Abstract : We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set converges in the Gromov–Hausdorff sense after a suitable rescaling to the Brownian continuum random tree. This confirms a conjecture by Aldous (1991). We also establish Benjamini–Schramm convergence of this model of random trees and provide a general approximation result, that allows for a transfer of a wide range of asymptotic properties of extremal and additive graph parameters from Pólya trees to unrooted trees.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01461633
Contributor : Benedikt Stufler Connect in order to contact the contributor
Submitted on : Wednesday, February 8, 2017 - 12:24:27 PM
Last modification on : Tuesday, November 19, 2019 - 12:22:25 PM
Long-term archiving on: : Tuesday, May 9, 2017 - 1:08:37 PM

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  • HAL Id : ensl-01461633, version 1
  • ARXIV : 1412.6333

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Benedikt Stufler. The continuum random tree is the scaling limit of unlabelled unrooted trees. 2017. ⟨ensl-01461633⟩

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