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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Janson, S. Left and Right Pathlengths in Random Binary Trees. Algorithmica 46, 419–429 (2006). https://doi.org/10.1007/s00453-006-0099-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-006-0099-3