# Asymptotics for the small fragments of the fragmentation at nodes

Abstract : We consider the fragmentation at nodes of the Lévy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time $\theta$. This limit is increasing in $\theta$ and discontinuous. In the $\alpha$-stable case the fragmentation is self-similar with index $1/\alpha$, with $\alpha \in (1,2)$ and the results are close to those Bertoin obtained for general self-similar fragmentations but with an additional assumtion which is not fulfilled here.
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Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2007, 13 (1), pp.211-228. 〈10.3150/07-BEJ6045〉
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https://hal.archives-ouvertes.fr/hal-00020262
Contributeur : Jean-François Delmas <>
Soumis le : mercredi 8 mars 2006 - 16:05:46
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : samedi 3 avril 2010 - 21:11:47

### Citation

Romain Abraham, Jean-François Delmas. Asymptotics for the small fragments of the fragmentation at nodes. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2007, 13 (1), pp.211-228. 〈10.3150/07-BEJ6045〉. 〈hal-00020262〉

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