{"paper":{"title":"Fourier dimension of Mandelbrot multiplicative cascades","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Bing Li, Changhao Chen, Ville Suomala","submitted_at":"2024-09-20T12:37:31Z","abstract_excerpt":"We investigate the Fourier dimension, $\\dim_F\\mu$, of Mandelbrot multiplicative cascade measures $\\mu$ on the $d$-dimensional unit cube. We show that if $\\mu$ is the cascade measure generated by a sub-exponential random variable then \\[\\dim_F\\mu=\\min\\{2,\\dim_2\\mu\\}\\,,\\] where $\\dim_2\\mu$ is the correlation dimension of $\\mu$ and it has an explicit formula.\n  For cascades on the circle $S\\subset\\mathbb{R}^2$, we obtain \\[\\dim_F\\mu\\ge\\frac{\\dim_2\\mu}{2+\\dim_2\\mu}\\,.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13455","kind":"arxiv","version":3},"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/2409.13455/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"}