The CRT is the scaling limit of unordered binary trees

Jean-François Marckert (1) , Grégory Miermont (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 ENS-PSL - École normale supérieure - Paris

We prove that a uniform, rooted unordered binary tree with $n$ vertices has the Brownian continuum random tree as its scaling limit for the Gromov-Hausdorff topology. The limit is thus, up to a constant factor, the same as that of uniform plane trees or labeled trees. Our analysis rests on a combinatorial and probabilistic study of appropriate trimming procedures of trees.

Domaines: Probabilités [math.PR]

Jean-François Marckert, Grégory Miermont. The CRT is the scaling limit of unordered binary trees. Random Structures and Algorithms, 2011, 38 (4), pp.467--501. ⟨hal-00364487⟩