Dislocation measure of the fragmentation of a general L\'evy tree

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].