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

2014/08/01 by Nicolas Broutin, Broutin, Nicolas, Minmin Wang +1
Decision Sciences · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1408.0144

openalex publication_date 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity

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