{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4LOZPA3LJAIK7OQQPBTUJN3ZA7","short_pith_number":"pith:4LOZPA3L","schema_version":"1.0","canonical_sha256":"e2dd97836b4810afba10786744b77907c63172cdbe8223f7f8aff2113efce393","source":{"kind":"arxiv","id":"1501.03264","version":1},"attestation_state":"computed","paper":{"title":"Spectral Analysis of a Discrete Metastable System Driven by L\\'evy Flights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Ilya Pavlyukevich, Toralf Burghoff","submitted_at":"2015-01-14T07:35:57Z","abstract_excerpt":"In this paper we consider a finite state time discrete Markov chain that mimics the behaviour of solutions of the stochastic differential equation $dX=-U'(X)dt+\\epsilon dL$, where $U$ is a multi-well potential with $n\\geq 2$ local minima and L is a symmetric \\alpha-stable L\\'evy process (L\\'evy flights process). We investigate the spectrum of the generator of this Markov chain in the limit $\\epsilon\\to 0$ and localize the top n eigenvalues $\\lambda^\\epsilon_1,\\dots, \\lambda^\\epsilon_n$. These eigenvalues turn out to be of the same algebraic order $O(\\epsilon^\\alpha)$ and are well separated fro"},"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":"1501.03264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-14T07:35:57Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"782480f7fa3935e6a3fbdc3bae19dcab1b7f4ee4e729e407b724820fb7743707","abstract_canon_sha256":"5b1ed6d6d4d30ccb64faf643278bb9d57e3d3b7f56e785c1d1c2a9e3c261b9c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:24.381686Z","signature_b64":"JN15+WlM0bz3w1C15lBJRU5yUnejV2cSW5GTJQnUGjPhA0T+l8diLTZtsJSrikd/EmwBwDkD8EMAorFUYzoxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2dd97836b4810afba10786744b77907c63172cdbe8223f7f8aff2113efce393","last_reissued_at":"2026-05-18T02:29:24.381348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:24.381348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Analysis of a Discrete Metastable System Driven by L\\'evy Flights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"math.PR","authors_text":"Ilya Pavlyukevich, Toralf Burghoff","submitted_at":"2015-01-14T07:35:57Z","abstract_excerpt":"In this paper we consider a finite state time discrete Markov chain that mimics the behaviour of solutions of the stochastic differential equation $dX=-U'(X)dt+\\epsilon dL$, where $U$ is a multi-well potential with $n\\geq 2$ local minima and L is a symmetric \\alpha-stable L\\'evy process (L\\'evy flights process). We investigate the spectrum of the generator of this Markov chain in the limit $\\epsilon\\to 0$ and localize the top n eigenvalues $\\lambda^\\epsilon_1,\\dots, \\lambda^\\epsilon_n$. These eigenvalues turn out to be of the same algebraic order $O(\\epsilon^\\alpha)$ and are well separated fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03264","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.03264","created_at":"2026-05-18T02:29:24.381398+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.03264v1","created_at":"2026-05-18T02:29:24.381398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03264","created_at":"2026-05-18T02:29:24.381398+00:00"},{"alias_kind":"pith_short_12","alias_value":"4LOZPA3LJAIK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4LOZPA3LJAIK7OQQ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4LOZPA3L","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7","json":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7.json","graph_json":"https://pith.science/api/pith-number/4LOZPA3LJAIK7OQQPBTUJN3ZA7/graph.json","events_json":"https://pith.science/api/pith-number/4LOZPA3LJAIK7OQQPBTUJN3ZA7/events.json","paper":"https://pith.science/paper/4LOZPA3L"},"agent_actions":{"view_html":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7","download_json":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7.json","view_paper":"https://pith.science/paper/4LOZPA3L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.03264&json=true","fetch_graph":"https://pith.science/api/pith-number/4LOZPA3LJAIK7OQQPBTUJN3ZA7/graph.json","fetch_events":"https://pith.science/api/pith-number/4LOZPA3LJAIK7OQQPBTUJN3ZA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7/action/storage_attestation","attest_author":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7/action/author_attestation","sign_citation":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7/action/citation_signature","submit_replication":"https://pith.science/pith/4LOZPA3LJAIK7OQQPBTUJN3ZA7/action/replication_record"}},"created_at":"2026-05-18T02:29:24.381398+00:00","updated_at":"2026-05-18T02:29:24.381398+00:00"}