{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EDIKZF5AVRHKNAMGWJOCANZ7TC","short_pith_number":"pith:EDIKZF5A","schema_version":"1.0","canonical_sha256":"20d0ac97a0ac4ea68186b25c20373f989813da9ab2d8ecfcab20b8496ffd8ff2","source":{"kind":"arxiv","id":"1108.5155","version":3},"attestation_state":"computed","paper":{"title":"Zeros and ratio asymptotics for matrix orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Holger Dette, Steven Delvaux","submitted_at":"2011-08-25T18:51:56Z","abstract_excerpt":"Ratio asymptotics for matrix orthogonal polynomials with recurrence coefficients $A_n$ and $B_n$ having limits $A$ and $B$ respectively (the matrix Nevai class) were obtained by Dur\\'an. In the present paper we obtain an alternative description of the limiting ratio. We generalize it to recurrence coefficients which are asymptotically periodic with higher periodicity, and/or which are slowly varying in function of a parameter. Under such assumptions, we also find the limiting zero distribution of the matrix orthogonal polynomials, generalizing results by Dur\\'an-L\\'opez-Saff and Dette-Reuther "},"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":"1108.5155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-08-25T18:51:56Z","cross_cats_sorted":[],"title_canon_sha256":"84653f7516eb475c3be1fa0949acf9e050a15ce8177d1c60d146faaaa8596260","abstract_canon_sha256":"9540f18a031f61ac8964e53787683fd91176bea216cf45cd4b701ae7a16b5c78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:05.403792Z","signature_b64":"/KjwVbrODcw+w0QAWBXUyurOncHzVZ+yy0WUUp92d8sRhQSwqqknge2Nkba2pm77yVf7l08wFkNKysXO1l2uBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20d0ac97a0ac4ea68186b25c20373f989813da9ab2d8ecfcab20b8496ffd8ff2","last_reissued_at":"2026-05-18T03:39:05.403230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:05.403230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zeros and ratio asymptotics for matrix orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Holger Dette, Steven Delvaux","submitted_at":"2011-08-25T18:51:56Z","abstract_excerpt":"Ratio asymptotics for matrix orthogonal polynomials with recurrence coefficients $A_n$ and $B_n$ having limits $A$ and $B$ respectively (the matrix Nevai class) were obtained by Dur\\'an. In the present paper we obtain an alternative description of the limiting ratio. We generalize it to recurrence coefficients which are asymptotically periodic with higher periodicity, and/or which are slowly varying in function of a parameter. Under such assumptions, we also find the limiting zero distribution of the matrix orthogonal polynomials, generalizing results by Dur\\'an-L\\'opez-Saff and Dette-Reuther "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5155","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":"1108.5155","created_at":"2026-05-18T03:39:05.403327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5155v3","created_at":"2026-05-18T03:39:05.403327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5155","created_at":"2026-05-18T03:39:05.403327+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDIKZF5AVRHK","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDIKZF5AVRHKNAMG","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDIKZF5A","created_at":"2026-05-18T12:26:28.662955+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/EDIKZF5AVRHKNAMGWJOCANZ7TC","json":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC.json","graph_json":"https://pith.science/api/pith-number/EDIKZF5AVRHKNAMGWJOCANZ7TC/graph.json","events_json":"https://pith.science/api/pith-number/EDIKZF5AVRHKNAMGWJOCANZ7TC/events.json","paper":"https://pith.science/paper/EDIKZF5A"},"agent_actions":{"view_html":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC","download_json":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC.json","view_paper":"https://pith.science/paper/EDIKZF5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5155&json=true","fetch_graph":"https://pith.science/api/pith-number/EDIKZF5AVRHKNAMGWJOCANZ7TC/graph.json","fetch_events":"https://pith.science/api/pith-number/EDIKZF5AVRHKNAMGWJOCANZ7TC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC/action/storage_attestation","attest_author":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC/action/author_attestation","sign_citation":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC/action/citation_signature","submit_replication":"https://pith.science/pith/EDIKZF5AVRHKNAMGWJOCANZ7TC/action/replication_record"}},"created_at":"2026-05-18T03:39:05.403327+00:00","updated_at":"2026-05-18T03:39:05.403327+00:00"}