# On the genealogy of conditioned stable Lévy forests

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00155592
Contributor : Juan Carlos Pardo Millan <>
Submitted on : Monday, June 18, 2007 - 4:10:58 PM
Last modification on : Friday, March 27, 2020 - 2:55:56 AM
Document(s) archivé(s) le : Thursday, April 8, 2010 - 6:00:06 PM

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• HAL Id : hal-00155592, version 1
• ARXIV : 0706.2605

### Citation

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

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