{"paper":{"title":"Exact dimensionality and projection properties of Gaussian multiplicative chaos measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.DS","math.MG","math.MP"],"primary_cat":"math.PR","authors_text":"Kenneth Falconer, Xiong Jin","submitted_at":"2016-01-04T16:27:37Z","abstract_excerpt":"Given a measure $\\nu$ on a regular planar domain $D$, the Gaussian multiplicative chaos measure of $\\nu$ studied in this paper is the random measure ${\\widetilde \\nu}$ obtained as the limit of the exponential of the $\\gamma$-parameter circle averages of the Gaussian free field on $D$ weighted by $\\nu$. We investigate the dimensional and geometric properties of these random measures. We first show that if $\\nu$ is a finite Borel measure on $D$ with exact dimension $\\alpha>0$, then the associated GMC measure ${\\widetilde \\nu}$ is non-degenerate and is almost surely exact dimensional with dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00556","kind":"arxiv","version":4},"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"}