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.

44 pages, 6 figures

References in corpus (6)

• Scaling limits of Markov branching trees with applications to Galton-Watson and random unordered trees
• The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity
• Cutting down trees with a Markov chainsaw
• Record process on the Continuum Random Tree
• Convergence of bi-measure R-tree and the pruning process
• Reversing the cut tree of the Brownian continuum random tree