The falling appart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation

Details The falling appart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation The falling appart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation

2008-11-28

arxiv.org/abs/0811.4754v1

Ann. Inst. H. Poincar\'e Probab. Statist., 45 (2009) No. 4, 1130-1149

Mathematics

Probability

23 pages, 4 figures, AMSLaTeX (PDFLaTeX), accepted in Annales de l'Institut Henri Poincar\'e (B)

Scientific paper

10.1214/08-AIHP304

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 fragmentation when it is about to reduce to dust are described in a limit theorem.

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