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

## TL;DR

This paper proves a central limit theorem for the bifurcation ratio in the Horton-Strahler branching model, extending previous results to general branch orders and providing new mathematical relations.

## Contribution

It generalizes the central limit theorem for bifurcation ratios to all branch orders, enhancing understanding of hierarchical branching structures.

## Key findings

- Established the central limit theorem for general branch order bifurcation ratios.
- Derived useful relations supporting the main theorems.
- Extended previous results from lowest to all branch orders.

## 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 bifurcation ratio of 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 are also derived in the proofs of the main theorems.