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 about to reduce to dust are described in a limit theorem.
@article{1257529896,
author = {Uribe Bravo, Ger\'onimo},
title = {The falling apart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 1130-1149},
language = {en},
url = {http://dml.mathdoc.fr/item/1257529896}
}
Uribe Bravo, Gerónimo. The falling apart of the tagged fragment and the asymptotic disintegration of the Brownian height fragmentation. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 1130-1149. http://gdmltest.u-ga.fr/item/1257529896/