{"paper":{"title":"The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boris Nectoux, Dorian Le Peutrec, Giacomo Di Ges\\`u, Tony Leli\\`evre","submitted_at":"2019-02-08T19:48:47Z","abstract_excerpt":"We consider the first exit point distribution from a bounded domain $\\Omega$ of the stochastic process $(X_t)_{t\\ge 0}$ solution to the overdamped Langevin dynamics $$d X_t = -\\nabla f(X_t) d t + \\sqrt{h} \\ d B_t$$ starting from the quasi-stationary distribution in $\\Omega$. In the small temperature regime ($h\\to 0$) and under rather general assumptions on $f$ (in particular, $f$ may have several critical points in $\\Omega$), it is proven that the support of the distribution of the first exit point concentrates on some points realizing the minimum of $f$ on $\\partial \\Omega$. The proof relies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03270","kind":"arxiv","version":1},"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"}