{"paper":{"title":"Fluctuations of stochastic PDEs with long-range correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Luca Gerolla, Martin Hairer, Xue-Mei Li","submitted_at":"2023-03-17T07:43:26Z","abstract_excerpt":"We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions $d \\geq 3$ with long-range dependence. This equation is driven by multiplicative Gaussian noise, which is white in time and coloured in space with non-integrable spatial covariance that decays at the rate of $|x|^{-\\kappa}$ at infinity, where $\\kappa \\in (2, d)$. Inspired by recent studies on SHE and KPZ equations driven by noise with compactly supported spatial correlation, we demonstrate that the correlations persist in the large-scale limit. The fluctuations of the diffusively scale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09811","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/2303.09811/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"}