{"paper":{"title":"Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chengbo Xiao, Guozheng Cheng, Hongdou Qu, Menghan Li, Xiang Fang, Yin Cai","submitted_at":"2026-06-07T15:35:06Z","abstract_excerpt":"We determine the Fourier dimension of the canonical dyadic Mandelbrot cascade on the unit interval under the minimal Kahane--Peyriere condition $W \\ge 0$, $\\mathbb{E}W=1$, $\\mathbb{E}[W\\log_2^+ W]<\\infty$, and $\\mathbb{E}[W\\log_2 W]<1$. Almost surely on non-extinction, $\\dim_F(\\mu)=\\dim_E(\\mu)=\\dim_2(\\mu)=\\sup_{1<q<2}\\max\\{0,2-(2/q)(1+\\log_2\\mathbb{E}[W^q])\\}$, with the convention that the corresponding term is zero when $\\mathbb{E}[W^q]=\\infty$. The proof is carried out in a vector-valued cascade model allowing arbitrary dependence between sibling weights; the classical independent cascade is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08683","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08683/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}