{"paper":{"title":"Metastability and time scales for parabolic equations with drift 2: the general time scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.AP"],"primary_cat":"math.PR","authors_text":"Claudio Landim, Insuk Seo, Jungkyoung Lee","submitted_at":"2024-02-12T15:02:00Z","abstract_excerpt":"Consider the elliptic operator given by \\[ \\mathscr{L}_\\epsilon f=b\\cdot\\nabla f+\\epsilon\\Delta f \\] for some smooth vector field $b:\\mathbb{R}^d\\to\\mathbb{R}^d$ and $\\epsilon>0$, and the initial-valued problem on $\\mathbb{R}^d$ \\[ \\left\\{\\begin{aligned}&\\partial_t u_\\epsilon=\\mathscr{L}_\\epsilon u_\\epsilon,\\\\ &u_\\epsilon(0,\\,\\cdot)=u_0(\\cdot), \\end{aligned} \\right. \\] for some bounded continuous function $u_0$. Under the hypothesis that the diffusion on $\\mathbb{R}^d$ induced by $\\mathscr{L}_\\epsilon$ has a Gibbs invariant measure of the form $\\exp \\{-U(x)/\\epsilon\\}dx$ for some smooth Morse "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07695","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/2402.07695/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"}