The exact packing measure of Lévy trees |
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Authors: | Thomas Duquesne |
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Institution: | Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, Boîte courrier 188, 4 place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | We study fine properties of Lévy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. Lévy trees are the scaling limits of Galton-Watson trees and they generalize the Aldous continuum random tree which corresponds to the Brownian case. In this paper, we prove that Lévy trees always have an exact packing measure: we explicitly compute the packing gauge function and we prove that the corresponding packing measure coincides with the mass measure up to a multiplicative constant. |
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Keywords: | primary 60G57 60J80 secondary 28A78 |
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