On the Contour of Random Trees

Abstract

Two stochastic processes describing the contour of simply generated random trees are studied: the contour process as defined by Gutjahr and Pflug [W. Gutjahr and G. Ch. Pflug, Stochastic Process. Appl., 41 (1992), pp. 69--89] and the traverse process constructed of the node heights during pre-order traversal of the tree. Using multivariate 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.