k-cut model for the Brownian Continuum Random Tree

2020/07/21 by Minmin Wang, Wang, Minmin
Decision Sciences · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2007.11080

openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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 n^1-1/2k, 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.

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