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

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.

References in corpus (1)

• Scaling limits of random planar maps with a unique large face

Cited by in corpus (2)

• Limits of subcritical random graphs and random graphs with excluded minors
• The Brownian continuum random tree as the unique solution to a fixed point equation