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.
Domains
Probability [math.PR]
Origin : Files produced by the author(s)
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