Globally centered discrete snakes
نویسنده
چکیده
We consider branching random walks built on Galton-Watson trees with offspring distribution having a bounded support, conditioned to have n nodes, and their rescaled convergences to the Brownian snake. We exhibit a notion of “globally centered discrete snake” that extends the usual settings in which the displacements are supposed centered. We show that under some additional moment conditions, when n goes to +∞, “globally centered discrete snakes” converge to the Brownian snake. The proof relies on a precise study of the “lineage” of the nodes in a Galton-Watson tree conditioned by the size, and their links with a multinomial process. Some consequences concerning Galton-Watson trees conditioned by the size are also derived. Subject classification : 60J80, 60F17, 60J65.
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