{"paper":{"title":"Uniform multifractal structure of stable trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paul Balan\\c{c}a","submitted_at":"2015-08-02T13:10:02Z","abstract_excerpt":"In this work, we investigate the spectrum of singularities of random stable trees with parameter $\\gamma\\in(1,2)$. We consider for that purpose the scaling exponents derived from two natural measures on stable trees: the local time $\\ell^a$ and the mass measure $\\textbf{m}$, providing as well a purely geometrical interpretation of the latter exponent. We first characterise the uniform component of the multifractal spectrum which exists at every level $a>0$ of stable trees and corresponds to large masses with scaling index $h\\in[\\tfrac{1+\\gamma}{\\gamma},\\tfrac{\\gamma}{\\gamma-1}]$ for the mass m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00229","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}