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

Ken Yamamoto*, Yoshihiro Yamazaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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

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


Dive into the research topics of 'Central limit theorem for the bifurcation ratio of a random binary tree'. Together they form a unique fingerprint.

Cite this