{"paper":{"title":"Flow equation approach to singular stochastic PDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Pawe{\\l} Duch","submitted_at":"2021-09-23T13:51:22Z","abstract_excerpt":"We prove universality of a macroscopic behavior of solutions of a large class of semi-linear parabolic SPDEs on $\\mathbb{R}_+\\times\\mathbb{T}$ with fractional Laplacian $(-\\Delta)^{\\sigma/2}$, additive noise and polynomial non-linearity, where $\\mathbb{T}$ is the $d$-dimensional torus. We consider the weakly non-linear regime and not necessarily Gaussian noises which are stationary, centered, sufficiently regular and satisfy some integrability and mixing conditions. We prove that the macroscopic scaling limit exists and has a universal law characterized by parameters of the relevant perturbati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11380","kind":"arxiv","version":3},"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/2109.11380/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"}