Asymptotics for the small fragments of the fragmentation at nodes

Authors
Type
Published Article
Publication Date
Mar 08, 2006
Submission Date
Mar 08, 2006
Identifiers
DOI: 10.3150/07-BEJ6045
arXiv ID: math/0603192
Source
arXiv
We consider the fragmentation at nodes of the L\'{e}vy 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.