{"paper":{"title":"Global well-posedness for general parabolic Anderson model on the whole plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Hao Shen, Rongchan Zhu, Xiangchan Zhu","submitted_at":"2026-06-25T07:13:39Z","abstract_excerpt":"For every $ 0<\\kappa<\\sqrt 5-2$, we prove global existence for the two-dimensional generalized parabolic Anderson model on the whole space $\\mathbb R^2$ with nonlinearity $F\\in C_b^2(\\mathbb R)$, driven by an enhanced noise $(\\eta,\\Psi)$. Here the noise $\\eta$ has polynomially weighted spatial Besov--H\\\"older regularity $-1-\\kappa$, and $\\Psi$ is the corresponding renormalized second-order object. If $F''$ is globally Lipschitz, the solution is unique.\n  The proof combines a weight-compatible annular high-low decomposition with a paracontrolled transport representation. The final remainder is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26681","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/2606.26681/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"}