On the Contour of Random Trees

Two stochastic processes describing the contour of simply generated random trees are studied: the contour process as deened by Gutjahr and PPug 9] and the traverse process constructed of the node heights during pre-order traversal of the tree. Using mul-tivariate generating functions and singularity analysis the weak convergence of the contour process to Brownian excursion is shown and a new proof of the analogous result for the traverse process is obtained.