## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab. Volume 20 (2015), paper no. 61, 14 pp.

Dates
Accepted: 8 September 2015
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465320988

Digital Object Identifier
doi:10.1214/ECP.v20-4250

Mathematical Reviews number (MathSciNet)
MR3399812

Zentralblatt MATH identifier
1328.60016

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 05C05: Trees

Rights

#### Citation

Albenque, Marie; Goldschmidt, Christina. The Brownian continuum random tree as the unique solution to a fixed point equation. Electron. Commun. Probab. 20 (2015), paper no. 61, 14 pp. doi:10.1214/ECP.v20-4250. https://projecteuclid.org/euclid.ecp/1465320988

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