{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SYYNV7A5OBJ5CW5UUC6OQH2YZT","short_pith_number":"pith:SYYNV7A5","schema_version":"1.0","canonical_sha256":"9630dafc1d7053d15bb4a0bce81f58cccf70f7df4e39818d0ccd76351f18241b","source":{"kind":"arxiv","id":"1308.4626","version":1},"attestation_state":"computed","paper":{"title":"A transience condition for a class of one-dimensional symmetric L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2013-08-21T16:33:15Z","abstract_excerpt":"In this paper, we give a sufficient condition for transience for a class of one-dimensional symmetric L\\'evy processes. More precisely, we prove that a one-dimensional symmetric L\\'evy process with the L\\'evy measure $\\nu(dy)=f(y)dy$ or $\\nu(\\{n\\})=p_n$, where the density function $f(y)$ is such that $f(y)>0$ a.e. and the sequence $\\{p_n\\}_{n\\geq1}$ is such that $p_n>0$ for all $n\\geq1$, is transient if $$\\int_1^{\\infty}\\frac{dy}{y^{3}f(y)}<\\infty\\quad\\textrm{or}\\quad \\sum_{n=1}^{\\infty}\\frac{1}{n^{3}p_n}<\\infty.$$ Similarly, we derive an analogous transience condition for one-dimensional symm"},"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":"1308.4626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-21T16:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"a568eec0b0f65193a409da2f1745140c34e9b445306735bfcbe03e866962549a","abstract_canon_sha256":"9fabaebb5230674998055a08630a14bdfe23e4c62053f3cc95988201b6847268"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.469896Z","signature_b64":"zhCHPtbID0VWOeaoHlRQDC1NwiO/tlt+EAD79uk7fSuK5YxL6aCy9/03++vqvSFyVAxa1Ifl+4tzcRKqoK+HCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9630dafc1d7053d15bb4a0bce81f58cccf70f7df4e39818d0ccd76351f18241b","last_reissued_at":"2026-05-18T03:15:21.469132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.469132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A transience condition for a class of one-dimensional symmetric L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2013-08-21T16:33:15Z","abstract_excerpt":"In this paper, we give a sufficient condition for transience for a class of one-dimensional symmetric L\\'evy processes. More precisely, we prove that a one-dimensional symmetric L\\'evy process with the L\\'evy measure $\\nu(dy)=f(y)dy$ or $\\nu(\\{n\\})=p_n$, where the density function $f(y)$ is such that $f(y)>0$ a.e. and the sequence $\\{p_n\\}_{n\\geq1}$ is such that $p_n>0$ for all $n\\geq1$, is transient if $$\\int_1^{\\infty}\\frac{dy}{y^{3}f(y)}<\\infty\\quad\\textrm{or}\\quad \\sum_{n=1}^{\\infty}\\frac{1}{n^{3}p_n}<\\infty.$$ Similarly, we derive an analogous transience condition for one-dimensional symm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4626","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":"1308.4626","created_at":"2026-05-18T03:15:21.469265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.4626v1","created_at":"2026-05-18T03:15:21.469265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4626","created_at":"2026-05-18T03:15:21.469265+00:00"},{"alias_kind":"pith_short_12","alias_value":"SYYNV7A5OBJ5","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SYYNV7A5OBJ5CW5U","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SYYNV7A5","created_at":"2026-05-18T12:27:59.945178+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/SYYNV7A5OBJ5CW5UUC6OQH2YZT","json":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT.json","graph_json":"https://pith.science/api/pith-number/SYYNV7A5OBJ5CW5UUC6OQH2YZT/graph.json","events_json":"https://pith.science/api/pith-number/SYYNV7A5OBJ5CW5UUC6OQH2YZT/events.json","paper":"https://pith.science/paper/SYYNV7A5"},"agent_actions":{"view_html":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT","download_json":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT.json","view_paper":"https://pith.science/paper/SYYNV7A5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.4626&json=true","fetch_graph":"https://pith.science/api/pith-number/SYYNV7A5OBJ5CW5UUC6OQH2YZT/graph.json","fetch_events":"https://pith.science/api/pith-number/SYYNV7A5OBJ5CW5UUC6OQH2YZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT/action/storage_attestation","attest_author":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT/action/author_attestation","sign_citation":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT/action/citation_signature","submit_replication":"https://pith.science/pith/SYYNV7A5OBJ5CW5UUC6OQH2YZT/action/replication_record"}},"created_at":"2026-05-18T03:15:21.469265+00:00","updated_at":"2026-05-18T03:15:21.469265+00:00"}