Topological self-similarity on the random binary-tree model
Mathematical Physics
2013-06-03 v1 math.MP
Abstract
Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.
Cite
@article{arxiv.0910.4795,
title = {Topological self-similarity on the random binary-tree model},
author = {Ken Yamamoto and Yoshihiro Yamazaki},
journal= {arXiv preprint arXiv:0910.4795},
year = {2013}
}