{"paper":{"title":"Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hendrik Weber, Martin Hairer","submitted_at":"2014-04-23T15:25:59Z","abstract_excerpt":"We study the stochastic Allen-Cahn equation driven by a noise term with intensity $\\sqrt{\\varepsilon}$ and correlation length $\\delta$ in two and three spatial dimensions. We study diagonal limits $\\delta, \\varepsilon \\to 0$ and describe fully the large deviation behaviour depending on the relationship between $\\delta$ and $\\varepsilon$.\n  The recently developed theory of regularity structures allows to fully analyse the behaviour of solutions for vanishing correlation length $\\delta$ and fixed noise intensity $\\varepsilon$. One key fact is that in order to get non-trivial limits as $\\delta \\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5863","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":""},"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"}