- Volume 13, Number 1 (2007), 211-228.
Asymptotics for the small fragments of the fragmentation at nodes
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.
Bernoulli Volume 13, Number 1 (2007), 211-228.
First available in Project Euclid: 30 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Abraham, Romain; Delmas, Jean-François. Asymptotics for the small fragments of the fragmentation at nodes. Bernoulli 13 (2007), no. 1, 211--228. doi:10.3150/07-BEJ6045. https://projecteuclid.org/euclid.bj/1175287730