Regularity of formation of dust in self-similar fragmentations
Behavior near the extinction time in self-similar fragmentations I : the stable case
The stable fragmentation with index of self-similarity ∈[−1/2, 0) is derived by looking at the masses of the subtrees formed by discarding the parts of a (1+)−1–stable continuum random tree below height , for ≥0. We give a detailed limiting description of the distribution of such a fragmentation, ((), ≥0), as it approaches its time of extinction, . In particular, we show that 1/ ((−)+) converges in distribution as →0 to a non-trivial limit. In order to prove this, we go further and...
The genealogy of self-similar fragmentations with negative index as a continuum random tree.
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