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 behaviour of 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 $α∈(1,2)$, and the results are close to those Bertoin obtained for general self-similar fragmentations but with an additional assumption which is not fulfilled here.
Citation
Romain Abraham. Jean-François Delmas. "Asymptotics for the small fragments of the fragmentation at nodes." Bernoulli 13 (1) 211 - 228, February 2007. https://doi.org/10.3150/07-BEJ6045
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