The exact packing measure of Lévy trees
Copyright policy )The exact packing measure of Lévy trees
We study fine properties of L��vy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. L��vy trees are the scaling limits of Galton-Watson trees and they generalize Aldous's continuum random tree which corresponds to the Brownian case. In this paper we prove that L��vy trees have always an exact packing measure: We explicitely compute the packing gauge function and we prove that the corresponding packing measure coincides with the mass measure up to a multiplicative constant.
33 pages
- Sorbonne Paris Cité France
- French National Centre for Scientific Research France
- University of Paris France
- Sorbonne University France
- UNIVERSITE PARIS DESCARTES France
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], packing measure, Applied Mathematics, branching processes, Probability (math.PR), Mass measure, Packing measure, Branching processes, Hausdorff and packing measures, Modelling and Simulation, Branching processes (Galton-Watson, birth-and-death, etc.), mass measure, FOS: Mathematics, Mathematics - Probability, Random measures, Lévy trees
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], packing measure, Applied Mathematics, branching processes, Probability (math.PR), Mass measure, Packing measure, Branching processes, Hausdorff and packing measures, Modelling and Simulation, Branching processes (Galton-Watson, birth-and-death, etc.), mass measure, FOS: Mathematics, Mathematics - Probability, Random measures, Lévy trees
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