We prove that the uniform unlabelled unrooted tree with $n$ vertices converges in the Gromov-Hausdorff sense after a suitable rescaling to the Brownian continuum random tree. This proves a conjecture by Aldous. We also treat the case of vertex-degree restrictions.
Schröder's problems and scaling limits of random trees
The Brownian continuum random tree as the unique solution to a fixed point equation
The CRT is the scaling limit of unordered binary trees
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