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Central limit theorem for the Horton–Strahler bifurcation ratio of general branch order

Part of: Limit theorems Graph theory Combinatorial probability

Published online by Cambridge University Press:  30 November 2017

Ken Yamamoto
Ken Yamamoto*
Affiliation:
University of the Ryukyus
*
* Postal address: Department of Physics and Earth Sciences, Faculty of Science, University of the Ryukyus, Senbaru 1, Nishihara, Okinawa, 903-0213, Japan. Email address: yamamot@sci.u-ryukyu.ac.jp
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Abstract

The Horton–Strahler ordering method, originating in hydrology, formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio. The main result of this paper is the central limit theorem for the bifurcation ratio of a general branch order. This is a generalized form of the central limit theorem for the lowest bifurcation ratio, which was previously proved. Some useful relations regarding the Horton–Strahler analysis are also derived in the proofs of the main theorems.

Keywords

Central limit theorembinary tree

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 05C05: Trees 60C05: Combinatorial probability

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1111 - 1124
Copyright
Copyright © Applied Probability Trust 2017 

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