Left and Right Pathlengths in Random Binary Trees

Authors:
Svante Janson
Affiliations:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06, Uppsala, Sweden
Venue:
Algorithmica
Year:
2006

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Abstract

We study the difference between the left and right total pathlengths in a random binary tree. The results include exact and asymptotic formulas for moments and an asymptotic distribution that can be expressed in terms of either the Brownian snake or ISE. The proofs are based on computing expectations for a subcritical binary Galton-Watson tree, and studying asymptotics as the Galton-Watson process approaches a critical one.