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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Abstract : We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Duquesne and Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is interesting in itself.

Keywords : Fragmentation Levy snake dislocation measure stable processes special Markov property

Author: Romain Abraham - Jean-François Delmas -



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