{"paper":{"title":"Oscillatory survival probability and eigenvalues of the non-self adjoint Fokker-Planck operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Holcman, Zeev Schuss","submitted_at":"2014-05-30T10:52:04Z","abstract_excerpt":"We demonstrate the oscillatory decay of the survival probability of the stochastic dynamics $d\\x_\\eps=\\mb{a}(\\x_\\eps)\\, dt +\\sqrt{2\\eps}\\,\\mb{b}(\\x_\\eps)\\,d\\w$, which is activated by small noise over the boundary of the domain of attraction $D$ of a stable focus of the drift $\\mb{a}(\\x)$. The boundary $\\p D$ of the domain is an unstable limit cycle of $\\mb{a}(\\x)$. The oscillations are explained by a singular perturbation expansion of the spectrum of the Dirichlet problem for the non-self adjoint Fokker-Planck operator in $D$ \\[L_\\eps u(\\x)=\\,\\eps\\sum_{i,j=1}^2 \\frac{\\p ^2\\left[ \\sigma ^{i,j}\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7821","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"}