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Asymptotics for the small fragments of the fragmentation at nodes

Romain Abraham·Jean-François Delmas
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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 $θ$. This limit is increasing in $θ$ and discontinuous. In the $α$-stable case the fragmentation is self-similar with index $1/α$, with $α\in (1,2)$ 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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Romain Abraham, Jean-François Delmas. 2006-03-08. Asymptotics for the small fragments of the fragmentation at nodes. https://doi.org/10.3150/07-bej6045

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