{"paper":{"title":"Conditional GMC within the stochastic heat flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeremy Clark, Li-Cheng Tsai","submitted_at":"2025-07-21T20:46:41Z","abstract_excerpt":"We establish that the family of polymer measures $M^{\\theta}_{[s,t]}$ associated with the Stochastic Heat Flow (SHF), indexed by $\\theta\\in\\mathbb{R}$, has a conditional Gaussian Multiplicative Chaos (GMC) structure. Namely, taking the random measure $M^{\\theta}_{[s,t]}$ as the reference measure, we construct the path-space GMC with noise strength $a > 0$ and prove that the resulting random measure is equal in law to $M^{\\theta+a}_{[s,t]}$. As two applications, we prove that the polymer measure and SHF tested against general nonnegative functions are almost surely strictly positive and that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16056","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/2507.16056/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"}