To model the destruction of a resilient network, Cai, Holmgren, Devroye and Skerman introduced the k-cut model on a random tree, as an extension to the classic problem of cutting down random trees. Berzunza, Cai and Holmgren later proved that the total number of cuts in the k-cut model to isolate the root of a Galton–Watson tree with a finite-variance offspring law and conditioned to have n nodes, when divided by , converges in distribution to some random variable defined on the Brownian CRT. We provide here a direct construction of the limit random variable, relying upon the Aldous–Pitman fragmentation process and a deterministic time change.
I am thankful to the anonymous referee and the editor for helpful suggestions.
"k-cut model for the Brownian continuum random tree." Electron. Commun. Probab. 26 1 - 11, 2021. https://doi.org/10.1214/21-ECP417