The exact packing measure of Lévy trees
Copyright policy )The exact packing measure of Lévy trees
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 Aldous's continuum random tree which corresponds to the Brownian case. In this paper we prove that Lévy 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
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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