Université de Versailles St-Quentin

The rotation correspondence is a map that sends the set of plane trees onto the set of binary trees. In this paper, we first show that when n goes to +∞, the image by the rotation correspondence of a uniformly chosen random plane tree τ with n nodes is close to 2τ (in a sense to be defined). The second part of the paper is devoted to the right and left depth of nodes in binary trees. We show that the empiric measure (suitably normalized) associated with the difference of the right depth and the left depth processes converges to the integrated super Brownian excursion. 1 Plane trees, binary trees and the rotation correspondence In this paper, we call plane tree a finite rooted unlabeled loop-free connected graph in which the set of children of every vertex is endowed with a total order. We denote by T Figure 1: Two different plane trees. n P the set of plane tree