English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we study the vertex cut-trees of Galton-Watson treesconditioned to have $n$ leaves. This notion is a slight variation ofDieuleveut's vertex cut-tree of Galton-Watson trees conditioned to have $n$vertices. Our main result is a joint Gromov-Hausdorff-Prokhorov convergence inthe finite variance case of the Galton-Watson tree and its vertex cut-tree toBertoin 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 tostrengthen Dieuleveut's and Bertoin and Miermont's Gromov-Prokhorov convergenceto Gromov-Hausdorff-Prokhorov remains open for their models conditioned to have$n$ vertices.

Gromov-Hausdorff-Prokhorov convergence of vertex cut-trees of n-leaf Galton-Watson trees