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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 [Abraham, Serlet] and for a tree without Brownian part [Abraham, Delmas].

preprint2010arXivOpen access
Guillaume Voisin
math.PR
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Guillaume Voisin

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