Gromov-Hausdorff -Prohorov convergence of vertex cut-trees of n-leaf Galton-Watson trees
主 题: Gromov-Hausdorff -Prohorov convergence of vertex cut-trees of n-leaf Galton-Watson trees
报告人: 何 辉 副教授 (北京师范大学)
时 间: 2016-10-10 15:00-16:00
地 点: 理科一号楼 1556(概率论系列报告)
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 fi nite 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 infi nite 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.
