Journal title
Bernoulli
DOI
10.3150/18-BEJ1055
Issue
3
Volume
25
Last updated
2022-03-06T17:47:42.27+00:00
Page
2301-2329
Abstract
In this paper, we study the vertex cut-trees 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–Prokhorov 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–Prokhorov convergence to Gromov–Hausdorff–Prokhorov remains open for their models conditioned to have n vertices.
Symplectic ID
859193
Submitted to ORA
On
Publication type
Journal Article
Publication date
12 June 2019