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On the genealogy of conditioned stable Lévy forests


We give a realization of the stable Lévy 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 Lévy process with no negative jumps and its height process.
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hal-00155592 , version 1 (18-06-2007)



Loic Chaumont, Juan Carlos Pardo Millan. On the genealogy of conditioned stable Lévy forests. 2007. ⟨hal-00155592⟩
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