The exact packing measure of Lévy trees

T. Duquesne (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study fine properties of Levy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. Levy 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 Levy 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

Domaines: Probabilités [math.PR]

T. Duquesne. The exact packing measure of Lévy trees. Stochastic Processes and their Applications, 2012, 122 (3), pp.968-1002. ⟨10.1016/j.spa.2011.10.013⟩. ⟨hal-00660184⟩