# Record process on the Continuum Random Tree

Abstract : By considering a continuous pruning procedure on Aldous's Brownian tree, we construct a random variable $\Theta$ which is distributed, conditionally given the tree, according to the probability law introduced by Janson as the limit distribution of the number of cuts needed to isolate the root in a critical Galton-Watson tree. We also prove that this random variable can be obtained as the a.s. limit of the number of cuts needed to cut down the subtree of the continuum tree spanned by $n$ leaves.
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https://hal.archives-ouvertes.fr/hal-00609467
Contributor : Romain Abraham <>
Submitted on : Friday, February 1, 2013 - 6:47:38 PM
Last modification on : Friday, May 4, 2018 - 1:17:27 AM
Document(s) archivé(s) le : Thursday, May 2, 2013 - 5:20:07 AM

### Files

record_2013_01.pdf
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### Identifiers

• HAL Id : hal-00609467, version 3
• ARXIV : 1107.3657

### Citation

Romain Abraham, Jean-François Delmas. Record process on the Continuum Random Tree. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10, pp.251. ⟨hal-00609467v3⟩

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