The cluster size distribution for a forest-fire process on .
The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation
We present a further analysis of the fragmentation at heights of the normalized brownian excursion. Specifically we study a representation for the mass of a tagged fragment in terms of a Doob transformation of the 1/2-stable subordinator and use it to study its jumps; this accounts for a description of how a typical fragment falls apart. These results carry over to the height fragmentation of the stable tree. Additionally, the sizes of the fragments in the brownian height fragmentation when it is...
The genealogy of self-similar fragmentations with negative index as a continuum random tree.
The law of the iterated logarithm for exchangeable random variables.
The lower envelope of positive self-similar Markov processes.