Central limit theorem for the bifurcation ratio of a random binary tree

Ken Yamamoto, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    2 Citations (Scopus)


    In order to formulate and examine the central limit theorem for a binary tree numerically, a method for generating random binary trees is presented. We first propose the correspondence between binary trees and a certain type of binary sequences (which we call Dyck sequences). Then, the method for generating random Dyck sequences is shown. Also, we propose the method of branch ordering of a binary tree by means of only the corresponding Dyck sequence. We confirm that the method is in good consistency with the topological analysis of binary trees known as the Horton-Strahler analysis. Two types of central limit theorem are numerically confirmed, and the obtained results are expressed in simple forms. Furthermore, the proposed method is available for a wide range of the topological analysis of binary trees.

    Original languageEnglish
    Article number415002
    JournalJournal of Physics A: Mathematical and Theoretical
    Issue number41
    Publication statusPublished - 2009


    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Modelling and Simulation
    • Statistics and Probability

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