### 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 |
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Pages (from-to) | 62-71 |

Number of pages | 10 |

Journal | Journal of Statistical Physics |

Volume | 139 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Mar 1 |

### 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

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## Cite this

Yamamoto, K., & Yamazaki, Y. (2010). Topological self-similarity on the random binary-tree model.

*Journal of Statistical Physics*,*139*(1), 62-71. https://doi.org/10.1007/s10955-010-9928-5