{"paper":{"title":"Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Justin Forlano, Leonardo Tolomeo","submitted_at":"2024-09-30T16:10:06Z","abstract_excerpt":"We consider the stochastic damped nonlinear wave equation $\\partial_t^{2}u+\\partial_t u+u-\\Delta u +u^{3} = \\sqrt{2} {\\langle{\\nabla}\\rangle^{-s}} \\xi$ on the two-dimensional torus $\\mathbb T^2$, where $\\xi$ denotes a space-time white noise and $s>0$. We show that the measure $\\vec{\\mu}_s$ corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20451","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/2409.20451/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"}