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

2015/04/21 by Marie Albenque, Albenque, Marie, Christina Goldschmidt +1
Economics, Econometrics and Finance · Mathematics · #05C05 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1504.05445

openalex publication_date 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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