Dislocation measure of the fragmentation of a general Lévy tree
Given a general critical or sub-critical branching mechanism and its associated Lévy 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 [R. Abraham and L. Serlet, 7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, 141 (2008) 113–154].