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

Nicolas Broutin (1, 2) , Minmin Wang (3, 2)

1 RAP - Networks, Algorithms and Probabilities
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 UPMC - Université Pierre et Marie Curie - Paris 6

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.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Probabilités [math.PR]

Nicolas Broutin, Minmin Wang. Cutting down $\mathbf p$-trees and inhomogeneous continuum random trees. Bernoulli, 2017, 23 (4A), pp.2380-2433. ⟨10.3150/16-BEJ813⟩. ⟨hal-01056125⟩