Reversing the cut tree of the Brownian continuum random tree

Abstract

Consider the Aldous--Pitman fragmentation process [Ann Probab, 26(4):1703--1726, 1998] of a Brownian continuum random tree ${\mathcal{T}}^{\mathrm{br}}$. The associated cut tree cut$({\mathcal{T}}^{\mathrm{br}})$, introduced by Bertoin and Miermont [Ann Appl Probab, 23:1469--1493, 2013], 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 cut$({\mathcal{T}}^{\mathrm{br}})$.

22 pages, 13 figures

References in corpus (2)

• Record process on the Continuum Random Tree
• Cutting edges at random in large recursive trees

Cited by in corpus (1)

• Cutting down $\mathbf{p}$-trees and inhomogeneous continuum random trees