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

Marie Albenque; Christina Goldschmidt

doi:10.1214/ECP.v20-4250

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

Marie Albenque
, Christina Goldschmidt

École Polytechnique

University of Oxford

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Electronic Communications in Probability
Volume	20
DOIs	https://doi.org/10.1214/ECP.v20-4250
Publication status	Published - 1 Jan 2015

Keywords

Brownian continuum random tree
Fixed point
Recursive distributional equation
Smoothing transform

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10.1214/ECP.v20-4250

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title = "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{\textquoteright} 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.",

keywords = "Brownian continuum random tree, Fixed point, Recursive distributional equation, Smoothing transform",

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AU - Goldschmidt, Christina

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N2 - 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.

AB - 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.

KW - Brownian continuum random tree

KW - Fixed point

KW - Recursive distributional equation

KW - Smoothing transform

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DO - 10.1214/ECP.v20-4250

M3 - Article

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SP - 1

EP - 14

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

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

Abstract

Keywords

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