# Cutting down $\mathbf p$-trees and inhomogeneous continuum random trees

Abstract : We study a fragmentation of the $\mathbf p$-trees of Camarri and Pitman [Elect. J. Probab., vol. 5, pp. 1--18, 2000]. We give exact correspondences between the $\mathbf p$-trees and trees which encode the fragmentation. We then use these results to study the fragmentation of the ICRTs (scaling limits of $\mathbf p$-trees) and give distributional correspondences between the ICRT and the tree encoding the fragmentation. The theorems for the ICRT extend the ones by Bertoin and Miermont [Ann. Appl. Probab., vol. 23(4), pp. 1469--1493, 2013] about the cut tree of the Brownian continuum random tree.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01056125
Contributor : Nicolas Broutin <>
Submitted on : Friday, August 15, 2014 - 1:06:20 PM
Last modification on : Tuesday, November 27, 2018 - 1:30:47 AM

### Identifiers

• HAL Id : hal-01056125, version 1
• ARXIV : 1408.0144

### Citation

Nicolas Broutin, Minmin Wang. Cutting down $\mathbf p$-trees and inhomogeneous continuum random trees. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2016. ⟨hal-01056125⟩

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