Dislocation measure of the fragmentation of a general L\'evy tree
Guillaume Voisin (MAPMO)
TL;DR
This paper introduces a method to analyze how a general Le9vy continuum random tree fragments under pruning, extending previous work on Brownian trees and trees without Brownian components.
Contribution
It computes the dislocation measures for fragmentation processes on general Le9vy trees, broadening the understanding of tree fragmentation beyond specific cases.
Findings
Derived explicit dislocation measures for Le9vy trees
Extended previous results from Brownian and non-Brownian trees
Provided a unified framework for tree fragmentation analysis
Abstract
Given a general critical or sub-critical branching mechanism and its associated L\'evy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [Abraham, Serlet] and for a tree without Brownian part [Abraham, Delmas].
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Stochastic processes and financial applications