Limit distribution of the quartet balance index for Aldous's b>=0-model

TL;DR

This paper introduces a new tree balance index and demonstrates its weak convergence to a fixed point distribution in Aldous's b>=0-model, providing theoretical insights into tree shape distributions.

Contribution

It defines a novel balance index for phylogenetic trees and characterizes its limiting distribution as a fixed point of a contraction operator.

Findings

Balance index converges weakly to a fixed point distribution.

The limiting distribution is characterized as a fixed point of a contraction operator.

Provides theoretical foundation for understanding tree shape distributions in Aldous's model.

Abstract

This paper builds up on T. Martinez-Coronado, A. Mir, F. Rossello and G. Valiente's work "A balance index for phylogenetic trees based on quartets", introducing a new balance index for trees. We show here that this balance index, in the case of Aldous's b>=0-model, convergences weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.