Central limit theorem for the bifurcation ratio of a random binary tree
Ken Yamamoto, Yoshihiro Yamazaki · Journal of Physics A Mathematical and Theoretical · 2009
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.