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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Consider the edge-deletion process in which the edges of some finite tree Tare removed one after the other in the uniform random order. Roughly speaking,the cut-tree then describes the genealogy of connected components appearing inthis edge-deletion process. Our main result shows that after a properrescaling, the cut-tree of a critical Galton-Watson tree with finite varianceand conditioned to have size n, converges as $n\to\infty$ to a Browniancontinuum random tree (CRT) in the weak sense induced by the Gromov-Prokhorovtopology. This yields a multi-dimensional extension of a limit theorem due toJanson [Random Structures Algorithms 29 (2006) 139-179] for the number ofrandom cuts needed to isolate the root in Galton-Watson trees conditioned bytheir sizes, and also generalizes a recent result [Ann. Inst. HenriPoincar\'{e} Probab. Stat. (2012) 48 909-921] obtained in the special case ofCayley trees.

The cut-tree of large Galton-Watson trees and the Brownian CRT