Electronic Journal of Probability

Reversing the cut tree of the Brownian continuum random tree

Nicolas Broutin and Minmin Wang

Full-text: Open access

Abstract

Consider the Aldous–Pitman fragmentation process [7] of a Brownian continuum random tree $\mathcal{T} ^{\mathrm{br} }$. The associated cut tree $\operatorname{cut} (\mathcal{T} ^{\mathrm{br} })$, introduced by Bertoin and Miermont [13], is defined in a measurable way from the fragmentation process, describing the genealogy of the fragmentation, and is itself distributed as a Brownian CRT. In this work, we introduce a shuffle transform, which can be considered as the reverse of the map taking $\mathcal{T} ^{\mathrm{br} }$ to $\operatorname{cut} (\mathcal{T} ^{\mathrm{br} })$.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 80, 23 pp.

Dates
Received: 4 November 2016
Accepted: 8 September 2017
First available in Project Euclid: 6 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1507255394

Digital Object Identifier
doi:10.1214/17-EJP105

Mathematical Reviews number (MathSciNet)
MR3710800

Zentralblatt MATH identifier
1379.60095

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60C05: Combinatorial probability
Secondary: 60G18: Self-similar processes 60F15: Strong theorems

Keywords
Brownian continuum random tree Aldous–Pitman fragmentation cut tree random cutting of random trees

Rights
Creative Commons Attribution 4.0 International License.

Citation

Broutin, Nicolas; Wang, Minmin. Reversing the cut tree of the Brownian continuum random tree. Electron. J. Probab. 22 (2017), paper no. 80, 23 pp. doi:10.1214/17-EJP105. https://projecteuclid.org/euclid.ejp/1507255394


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