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2021 k-cut model for the Brownian continuum random tree
Minmin Wang
Author Affiliations +
Electron. Commun. Probab. 26: 1-11 (2021). DOI: 10.1214/21-ECP417


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 n112k, 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.


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Minmin Wang. "k-cut model for the Brownian continuum random tree." Electron. Commun. Probab. 26 1 - 11, 2021.


Received: 24 July 2020; Accepted: 30 June 2021; Published: 2021
First available in Project Euclid: 16 July 2021

arXiv: 2007.11080
Digital Object Identifier: 10.1214/21-ECP417

Primary: 60C05 , 60G18 , 60G55

Keywords: Brownian excursion , Continuum random tree , random cut on random tree


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