# Large deviation theorem for branches of the random binary tree in the Horton-Strahler analysis

## TL;DR

This paper establishes a large deviation theorem for the distribution of branch orders in random binary trees using Horton-Strahler analysis, providing asymptotic rate functions for deviations.

## Contribution

It introduces a large deviation theorem specific to branch order counts in random binary trees, with asymptotic analysis of the rate functions.

## Key findings

- Large deviation theorem for branch counts in random binary trees
- Asymptotic forms of the rate functions are derived
- Provides a theoretical foundation for analyzing bifurcation complexity

## Abstract

The Horton-Strahler analysis is a graph-theoretic method to measure the bifurcation complexity of branching patterns, by defining a number called the order to each branch. The main result of this paper is a large deviation theorem for the number of branches of each order in a random binary tree. The rate function associated with a large deviation cannot be derived in a closed form; instead, asymptotic forms of the rate function are given.