Topological self-similarity on the random binary-tree model

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

2009-10-26

arxiv.org/abs/0910.4795v1

J. Stat. Phys. 139 (2010), pp. 62-71

Physics

Mathematical Physics

Scientific paper

10.1007/s10955-010-9928-5

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.

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