# Topological self-similarity on the random binary-tree model

Ken Yamamoto, Yoshihiro Yamazaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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.

Original language English 62-71 10 Journal of Statistical Physics 139 1 https://doi.org/10.1007/s10955-010-9928-5 Published - 2010 Mar

### Fingerprint

Random Trees
Binary Tree
Self-similarity
Hierarchical Structure
Asymptotic Analysis
Statistical property
Branching
Quantify
Branch
Model
Generalization

### Keywords

• Asymptotic behavior
• Binary tree
• Branching pattern
• Hierarchical structure
• Horton-Strahler analysis
• Topological self-similarity

### ASJC Scopus subject areas

• Statistical and Nonlinear Physics
• Mathematical Physics

### Cite this

In: Journal of Statistical Physics, Vol. 139, No. 1, 03.2010, p. 62-71.

Research output: Contribution to journalArticle

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