The cut-tree of large recursive trees
type: Dataset
description: Imagine a graph which is progressively destroyed by cutting its edges one after the other in a uniform random order. The so-called cut-tree records key steps of this destruction process. It can be viewed as a random metric space equipped with a natural probability mass. In this work, we show that the cut-tree of a random recursive tree of size $n$, rescaled by the factor $n^{-1}\ln n$, converges in probability as $n\to \infty$ in the sense of Gromov-Hausdorff-Prokhorov, to the unit interval endowed with the usual distance and Lebesgue measure. This enables us to explain and extend some recent results of Kuba and Panholzer on multiple isolation of nodes in random recursive trees.
issued: 2026-05-09T20:08:29.479452
language: en
modified: 2026-05-09T20:08:29.479456
contact point: Organization
  fn: CCSD
keyword: 60f15-05c05
keyword: destruction-of-graphs
keyword: gromov-hausdorff-prokhorov-convergence
keyword: infoeu-reposemanticspreprint
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: multiple-isolation-of-nodes
keyword: preprints-working-papers-
keyword: random-recursive-tree
landing page: https://hal.science/hal-00859385

The cut-tree of large recursive trees
type: Distribution
format: HTML
issued: 2026-05-09T20:08:29.480716
modified: 2026-05-09T20:08:29.469838
access URL: https://hal.science/hal-00859385

test_moissonnage_selune
type: Agent