English

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

Probability 2016-12-15 v4

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.

Keywords

Cite

@article{arxiv.1412.6333,
  title  = {The continuum random tree is the scaling limit of unlabelled unrooted trees},
  author = {Benedikt Stufler},
  journal= {arXiv preprint arXiv:1412.6333},
  year   = {2016}
}