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

2014/12/19 by Stufler, Benedikt
#05C80 #60F17 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1412.6333

Abstract

We prove 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 proves a conjecture by Aldous. Moreover, we establish Benjamini-Schramm convergence of this model of random trees.

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