{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2TI3JCLM5FWPG3RBI3ZW6KHU5R","short_pith_number":"pith:2TI3JCLM","schema_version":"1.0","canonical_sha256":"d4d1b4896ce96cf36e2146f36f28f4ec70509f15a9cd4ef66999a048ed20864f","source":{"kind":"arxiv","id":"1508.06659","version":3},"attestation_state":"computed","paper":{"title":"Persistence of Gaussian processes: non-summable correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Sumit Mukherjee","submitted_at":"2015-08-26T20:49:11Z","abstract_excerpt":"Suppose the auto-correlations of real-valued, centered Gaussian process $Z(\\cdot)$ are non-negative and decay as $\\rho(|s-t|)$ for some $\\rho(\\cdot)$ regularly varying at infinity of order $-\\alpha \\in [-1,0)$. With $I_\\rho(t)=\\int_0^t \\rho(s)ds$ its primitive, we show that the persistence probabilities decay rate of $ -\\log\\mathbb{P}(\\sup_{t \\in [0,T]}\\{Z(t)\\}<0)$ is precisely of order $(T/I_\\rho(T)) \\log I_\\rho(T)$, thereby closing the gap between the lower and upper bounds of \\cite{NR}, which stood as such for over fifty years. We demonstrate its usefulness by sharpening recent results of \\"},"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":"1508.06659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-26T20:49:11Z","cross_cats_sorted":[],"title_canon_sha256":"145837eb8183bc3d8d6c77b63d5dd6d63a92a39a46f39f835b7e342d423d436d","abstract_canon_sha256":"6cda3275ebadbb17a8c3c4e5e3956df97bfeb963b50ecd3db1eb2cc32fae3602"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:53.974032Z","signature_b64":"F1OGc1vMjDdBXEkWjeL9ZfOStVtDWSFrOF7jfZyTFedU8uOpHvnMf1xkOGsFt6eCar37CD4zBhqakB2oWnyMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4d1b4896ce96cf36e2146f36f28f4ec70509f15a9cd4ef66999a048ed20864f","last_reissued_at":"2026-05-18T01:04:53.973486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:53.973486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Persistence of Gaussian processes: non-summable correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Sumit Mukherjee","submitted_at":"2015-08-26T20:49:11Z","abstract_excerpt":"Suppose the auto-correlations of real-valued, centered Gaussian process $Z(\\cdot)$ are non-negative and decay as $\\rho(|s-t|)$ for some $\\rho(\\cdot)$ regularly varying at infinity of order $-\\alpha \\in [-1,0)$. With $I_\\rho(t)=\\int_0^t \\rho(s)ds$ its primitive, we show that the persistence probabilities decay rate of $ -\\log\\mathbb{P}(\\sup_{t \\in [0,T]}\\{Z(t)\\}<0)$ is precisely of order $(T/I_\\rho(T)) \\log I_\\rho(T)$, thereby closing the gap between the lower and upper bounds of \\cite{NR}, which stood as such for over fifty years. We demonstrate its usefulness by sharpening recent results of \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06659","kind":"arxiv","version":3},"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":"1508.06659","created_at":"2026-05-18T01:04:53.973557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06659v3","created_at":"2026-05-18T01:04:53.973557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06659","created_at":"2026-05-18T01:04:53.973557+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TI3JCLM5FWP","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TI3JCLM5FWPG3RB","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TI3JCLM","created_at":"2026-05-18T12:29:02.477457+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/2TI3JCLM5FWPG3RBI3ZW6KHU5R","json":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R.json","graph_json":"https://pith.science/api/pith-number/2TI3JCLM5FWPG3RBI3ZW6KHU5R/graph.json","events_json":"https://pith.science/api/pith-number/2TI3JCLM5FWPG3RBI3ZW6KHU5R/events.json","paper":"https://pith.science/paper/2TI3JCLM"},"agent_actions":{"view_html":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R","download_json":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R.json","view_paper":"https://pith.science/paper/2TI3JCLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06659&json=true","fetch_graph":"https://pith.science/api/pith-number/2TI3JCLM5FWPG3RBI3ZW6KHU5R/graph.json","fetch_events":"https://pith.science/api/pith-number/2TI3JCLM5FWPG3RBI3ZW6KHU5R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R/action/storage_attestation","attest_author":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R/action/author_attestation","sign_citation":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R/action/citation_signature","submit_replication":"https://pith.science/pith/2TI3JCLM5FWPG3RBI3ZW6KHU5R/action/replication_record"}},"created_at":"2026-05-18T01:04:53.973557+00:00","updated_at":"2026-05-18T01:04:53.973557+00:00"}