Asymptotic degree distribution in random recursive trees

Authors:
Svante Janson
Affiliations:
Department of Mathematics, Uppsala University, P.O. Box 480, S-751 06 Uppsala, Sweden
Venue:
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Year:
2005

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Abstract

The distributions of vertex degrees in random recursive trees and random plane recursive trees are shown to be asymptotically normal. Formulas are given for the asymptotic variances and covariances of the number of vertices with given outdegrees. We also give functional limit theorems for the evolution as vertices are added. The proofs use some old and new results about generalized Pólya urn models. We consider generalized Pólya urns with infinitely many types, but reduce them to the finite type case. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005