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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}\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.7821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T10:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"0b137114c11a9ed4592ea307d315e186c91c762dc366f3cce00d8dc2662879db","abstract_canon_sha256":"0496a21bc44059b925f696c1be5508e029a029a08bc3b6e96b73057bcfb8c286"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:49.758045Z","signature_b64":"EPtBxgDsvgcYX2S72sC+UqDUEtYbvII1SMKXdhfwle4xeSRMMIMuZ2twKzEIiTKt6ySdzUak0l8jVuGo+e4FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99356b0a2bb93508412d78899fa72979b70bd8b0d0b719cbe24c8452df6baee5","last_reissued_at":"2026-05-18T02:50:49.757481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:49.757481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mb{a}(\\x)$. 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