2005/09/22 by Thomas Duquesne, Duquesne, Thomas, Matthias Winkel +1 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #G22 #G3 #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:G22 #msc:G3
paper · pdf · doi:10.48550/arxiv.math/0509518
49 pages; 1 figure
arxiv created 2005/09/22 · openalex publication_date 2005/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct random locally compact real trees called Levy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton-Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Levy tree as the limit of this growing family with respect to the Gromov-Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Levy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure.