{"paper":{"title":"Renormalisation in the presence of variance blowup","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martin Hairer","submitted_at":"2024-01-19T18:15:30Z","abstract_excerpt":"We show that if one drives the KPZ equation by the derivative of a space-time white noise smoothened out at scale $\\varepsilon \\ll 1$ and multiplied by $\\varepsilon^{3/4}$ then, as $\\varepsilon \\to 0$, solutions converge to the Cole-Hopf solutions to the KPZ equation driven by space-time white noise.\n  In the same vein, we also show that if one drives an SDE by fractional Brownian motion with Hurst parameter $H < 1/4$, smoothened out at scale $\\varepsilon \\ll 1$ and multiplied by $\\varepsilon^{1/4-H}$ then, as $\\varepsilon \\to 0$, solutions converge to an SDE driven by white noise. The mechani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.10868","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.10868/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"}