T:A:L:K:S

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title:
Hausdorff and packing measures of Levy trees
name:
Duquesne
first name:
Thomas
location/conference:
levy10
abstract:
In this paper we discuss Hausdorff and packing measures of random continuous trees called
L\\\'evy trees . L\\\'evy trees have been introduced by Le Gall and Le Jan in 1998. Aldous\'s continuum random tree 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. We also prove that L\\\'evy trees have an exact packing measure.



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\\address{Thomas Duquesne, LPMA, Universit\\\'e P. et M. Curie, 4 place Jussieu, Boite 188, 75252 Paris Cedex 05, FRANCE.}

\\email{thomas.duquesne at upmc.fr}