{"paper":{"title":"Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.PR","authors_text":"Yanqi Qiu, Yukun Chen, Zhaofeng Lin","submitted_at":"2025-07-31T12:28:43Z","abstract_excerpt":"We determine the exact values of the Fourier dimensions for Gaussian Multiplicative Chaos measures on the $d$-dimensional torus $\\mathbb{T}^d$ for all integers $d \\ge 1$. This resolves a problem left open in previous works [LQT24,LQT25] for high dimensions $d\\ge 3$. The proof relies on a new construction of log-correlated Gaussian fields admitting specific decompositions into smooth processes with high regularity. This construction enables a multi-resolution analysis to obtain sharp local estimates on the measure's Fourier decay. These local estimates are then integrated into a global bound us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23494","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/2507.23494/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"}