{"paper":{"title":"The Gaussian structure of a perturbed KPZ","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tomasz Komorowski, Yu Gu","submitted_at":"2026-06-05T15:02:13Z","abstract_excerpt":"We study the KPZ equation on a circle with an additive spatial perturbation $\\partial_t h=\\tfrac12\\Delta h+\\tfrac12|\\nabla h|^2+\\xi+ V$, where $\\xi$ is a spacetime white noise and $V$ is a smooth spatial function. When $V=0$, it is well-known that the unique invariant measure is the Brownian bridge. In the presence of the perturbation, we show that the equation admits a unique invariant measure that is absolutely continuous with respect to the Brownian bridge. We further prove the measure has a finite relative entropy with respect to the law of the bridge and that, for any $p\\in(1,\\infty)$, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07353","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/2606.07353/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"}