Packing and Hausdorff measures of stable trees.

Abstract : In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of Lévy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).
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Pré-publication, Document de travail
40 pages. 2010
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https://hal.archives-ouvertes.fr/hal-00451064
Contributeur : Thomas Duquesne <>
Soumis le : jeudi 28 janvier 2010 - 10:26:57
Dernière modification le : mercredi 12 octobre 2016 - 01:03:06
Document(s) archivé(s) le : vendredi 18 juin 2010 - 16:58:07

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Levytrees_stable.pdf
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  • HAL Id : hal-00451064, version 1
  • ARXIV : 1001.5329

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UPMC | PMA | INSMI | USPC

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Thomas Duquesne. Packing and Hausdorff measures of stable trees.. 40 pages. 2010. <hal-00451064>

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