The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation

Gerónimo Uribe Bravo

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1130-1149
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Uribe Bravo, Gerónimo. "The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1130-1149. <http://eudml.org/doc/78057>.

@article{UribeBravo2009,
abstract = {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.},
author = {Uribe Bravo, Gerónimo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self-similar fragmentation; normalized brownian excursion; Self-similar fragmentation; normalized Brownian excursion; stable subordinator},
language = {eng},
number = {4},
pages = {1130-1149},
publisher = {Gauthier-Villars},
title = {The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation},
url = {http://eudml.org/doc/78057},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Uribe Bravo, Gerónimo
TI - The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1130
EP - 1149
AB - 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.
LA - eng
KW - self-similar fragmentation; normalized brownian excursion; Self-similar fragmentation; normalized Brownian excursion; stable subordinator
UR - http://eudml.org/doc/78057
ER -

References

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