Electronic Communications in Probability

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

Marie Albenque and Christina Goldschmidt

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

continuum random tree fixed point equation

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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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