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 $\operatorname{cut} (\mathcal{T} ^{\mathrm{br} })$.
Citation
Nicolas Broutin. Minmin Wang. "Reversing the cut tree of the Brownian continuum random tree." Electron. J. Probab. 22 1 - 23, 2017. https://doi.org/10.1214/17-EJP105
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