{"paper":{"title":"Metastability and time scales for parabolic equations with drift 1: the first 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":"2023-09-11T15:32:14Z","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\\colon \\mathbb R^d \\to\\mathbb R^d$ and a small parameter $\\epsilon>0$. Consider the initial-valued problem $$ \\left\\{ \\begin{aligned} &\\partial_ t u_\\epsilon = \\mathscr L_\\epsilon u_\\epsilon,\\\\ &u_\\epsilon (0, \\cdot) = u_0(\\cdot), \\end{aligned} \\right. $$ for some bounded continuous function $u_0$. Denote by $\\mathcal M_0$ the set of critical points of $b$ which are stable stationary points for the ODE $\\dot x (t) = b (x(t))$. Under the hypothesis that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05546","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.05546/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"}