{"paper":{"title":"Random sparse sampling in a Gibbs weighted tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Julien Barral, St\\'ephane Seuret","submitted_at":"2015-12-14T15:45:15Z","abstract_excerpt":"Let $\\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\\Sigma=\\{0,1\\}^{\\mathbb{N}}$ associated with a H\\\"older potential. The thermodynamic and multifractal properties of $\\mu$ are well known to be linked via the multifractal formalism. In this article, the impact of a random sampling procedure on this structure is studied.\n  More precisely, let $\\{I_w\\}_{w\\in \\Sigma^*}$ stand for the collection of dyadic subintervals of $[0,1]$ naturally indexed by the set of finite dyadic words $\\Sigma^*$. Fix $\\eta\\in(0,1)$, and a sequence $(p_w)_{w\\in \\Sigma^*}$ of independent Bernoulli v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04368","kind":"arxiv","version":1},"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"}