On the genealogy on conditioned stable Lévy forest

Details On the genealogy on conditioned stable Lévy forest On the genealogy on conditioned stable Lévy forest

2007-06-18

arxiv.org/abs/0706.2605v1

Mathematics

Probability

Scientific paper

We give a realization of the stable L\'evy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent Galton-Watson trees whose offspring distribution is in the domain of attraction of any stable law conditioned on their total progeny to be equal to $n$. We prove that when $n$ and $k$ tend towards $+\infty$, under suitable rescaling, the associated coding random walk, the contour and height processes converge in law on the Skorokhod space respectively towards the "first passage bridge" of a stable L\'evy process with no negative jumps and its height process.

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