Open Access
2017 Reversing the cut tree of the Brownian continuum random tree
Nicolas Broutin, Minmin Wang
Electron. J. Probab. 22: 1-23 (2017). DOI: 10.1214/17-EJP105


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 $\operatorname{cut} (\mathcal{T} ^{\mathrm{br} })$.


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Nicolas Broutin. Minmin Wang. "Reversing the cut tree of the Brownian continuum random tree." Electron. J. Probab. 22 1 - 23, 2017.


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

zbMATH: 1379.60095
MathSciNet: MR3710800
Digital Object Identifier: 10.1214/17-EJP105

Primary: 60C05 , 60J80
Secondary: 60F15 , 60G18

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

Vol.22 • 2017
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