2005/09/29 by Thomas Duquesne, Duquesne, Thomas, Jean‐François Le Gall +2
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.math/0509690
25 pages
arxiv created 2005/09/29 · openalex publication_date 2005/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study fine properties of the so-called stable trees, which are the scaling limits of critical Galton-Watson trees conditioned to be large. In particular we derive the exact Hausdorff measure function for Aldous' continuum random tree and for its level sets. It follows that both the uniform measure on the tree and the local time measure on a level set coincide with certain Hausdorff measures. Slightly less precise results are obtained for the Hausdorff measure of general stable trees.