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Tuesday, March 7, 2017

**Abstract:** We study the vertex cut-tree of Galton-Watson trees conditioned to have n leaves. This notion is a slight variation of Dieuleveut's vertex cut-tree of Galton-Watson trees conditioned to have n vertices. Our main result is a joint Gromov-Hausdorff -Prohorov convergence in the finite variance case of the Galton-Watson tree and its vertex cut-tree to Bertoin and Miermont's joint distribution of the Brownian CRT and its cut-tree. The methods also apply to the infinite variance case, but the problem to strengthen Dieuleveut's and Bertoin and Miermont's Gromov-Prohorov convergence to Gromov-Hausdorff-Prohorov remains open for their models conditioned to have n vertices. This is a joint work with Matthias Winkel.

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