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• W3100171672 abstract "Consider the edge-deletion process in which the edges of some finite tree $T$ are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton–Watson tree with finite variance and conditioned to have size $n$, converges as $ntoinfty$ to a Brownian continuum random tree (CRT) in the weak sense induced by the Gromov–Prokhorov topology. This yields a multi-dimensional extension of a limit theorem due to Janson [Random Structures Algorithms 29 (2006) 139–179] for the number of random cuts needed to isolate the root in Galton–Watson trees conditioned by their sizes, and also generalizes a recent result [Ann. Inst. Henri Poincaré Probab. Stat. (2012) 48 909–921] obtained in the special case of Cayley trees." @default.
• W3100171672 created "2020-11-23" @default.
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• W3100171672 date "2013-08-01" @default.
• W3100171672 modified "2023-09-25" @default.
• W3100171672 title "The cut-tree of large Galton–Watson trees and the Brownian CRT" @default.
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• W3100171672 doi "https://doi.org/10.1214/12-aap877" @default.
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