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

Ken Yamamoto*, Yoshihiro Yamazaki


研究成果: Article査読

2 被引用数 (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.

ジャーナルJournal of Physics A: Mathematical and Theoretical
出版ステータスPublished - 2009

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)


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