The Brownian continuum random tree as the unique solution to a fixed point equation

TL;DR

This paper characterizes the Brownian continuum random tree as the unique fixed point of a natural recursive operation, demonstrating its attractiveness and providing a new perspective on its structure.

Contribution

It introduces a novel fixed point characterization of the Brownian continuum random tree through a recursive distributional equation.

Findings

The Brownian continuum random tree is the unique fixed point of a specific recursive operation.

The fixed point is shown to be attractive, indicating stability.

Provides a new recursive perspective on the structure of the CRT.

Abstract

In this note, we provide a new characterization of Aldous' Brownian continuum random tree as the unique fixed point of a certain natural operation on continuum trees (which gives rise to a recursive distributional equation). We also show that this fixed point is attractive.