{"paper":{"title":"Interface fluctuations for $1$D stochastic Allen-Cahn equation -- singular regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Shuhan Zhou, Weijun Xu","submitted_at":"2025-08-21T07:29:35Z","abstract_excerpt":"We study interface fluctuations for the $1$D stochastic Allen-Cahn equation perturbed by half a spatial derivative of the spacetime white noise. This half derivative makes the solution distribution-valued, so that proper renormalization is needed to make sense of the solution.\n  We show that if the noise is sufficiently small, then an analogue of the classical results by \\cite{Fun95,BBDMP98} holds in this singular regime. More precisely, for initial data close to the traveling wave solution of the deterministic equation, under proper long time scaling, the solution still stays close to the fam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.15319","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/2508.15319/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"}