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The exact packing measure of Lévy trees

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  • Duquesne, Thomas

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.

Suggested Citation

  • Duquesne, Thomas, 2012. "The exact packing measure of Lévy trees," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 968-1002.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:968-1002
    DOI: 10.1016/j.spa.2011.10.013
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    References listed on IDEAS

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    1. Bingham, N. H., 1976. "Continuous branching processes and spectral positivity," Stochastic Processes and their Applications, Elsevier, vol. 4(3), pages 217-242, August.
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