{"paper":{"title":"Field-measure correspondence in Liouville quantum gravity almost surely commutes with all conformal maps simultaneously","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Menglu Wang, Scott Sheffield","submitted_at":"2016-05-19T23:20:24Z","abstract_excerpt":"In Liouville quantum gravity (or $2d$-Gaussian multiplicative chaos) one seeks to define a measure $\\mu^h = e^{\\gamma h(z)} dz$ where $h$ is an instance of the Gaussian free field on a planar domain $D$. Since $h$ is a distribution, not a function, one needs a regularization procedure to make this precise: for example, one may let $h_\\epsilon(z)$ be the average value of $h$ on the circle of radius $\\epsilon$ centered at $z$ (or an analogous average defined using a bump function supported inside that circle) and then write $\\mu^h = \\lim_{\\epsilon \\to 0} \\epsilon^{\\frac{\\gamma^2}{2}} e^{\\gamma h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06171","kind":"arxiv","version":2},"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"}