{"paper":{"title":"Eyring-Kramers exit rates for the overdamped Langevin dynamics: the case with saddle points on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Boris Nectoux, Dorian Le Peutrec, Tony Leli\\`evre","submitted_at":"2022-07-19T14:05:13Z","abstract_excerpt":"Let $(X_t)_{t\\ge 0}$ be the stochastic process solution to the overdamped Langevin dynamics\n  $$dX_t=-\\nabla f(X_t) \\, dt +\\sqrt h \\, dB_t$$ and let $\\Omega \\subset \\mathbb R^d $ be the basin of attraction of a local minimum of $f: \\mathbb R^d \\to \\mathbb R$. Up to a small perturbation of $\\Omega$ to make it smooth, we prove that the exit rates of $(X_t)_{t\\ge 0}$ from $\\Omega$ through each of the saddle points of $f$ on $\\partial \\Omega$ can be parametrized by the celebrated Eyring-Kramers laws, in the limit $h \\to 0$. This result provides firm mathematical grounds to jump Markov models which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.09284","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.09284/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"}