{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RMA3PAEEVQADQMKFLDOYBL5XOQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7697a4cdcd0514a8aacc82f6a99fad697f865124fb1f770e0378ddce16bcd970","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-05-24T14:46:31Z","title_canon_sha256":"dfee211290e967fc1cf809c2b96c4f3531a27d7b31ecb1318b475da5358e9e36"},"schema_version":"1.0","source":{"id":"1905.10265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10265","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10265v1","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10265","created_at":"2026-05-17T23:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"RMA3PAEEVQAD","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RMA3PAEEVQADQMKF","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RMA3PAEE","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:64b46cd758c4869a7c90add2aa72ae5c502af7fbc53276e7482151184ddef7cb","target":"graph","created_at":"2026-05-17T23:45:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the spectra of general $N\\times N$ Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime $N\\gg 1$. We prove an asymptotic formula for the number of eigenvalues of the perturbed matrix in smooth domains. We show that these eigenvalues follow a Weyl law with probability sub-exponentially close to $1$, as $N\\gg1$, in particular that most eigenvalues of the perturbed Toeplitz matrix are close to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.","authors_text":"Johannes Sjoestrand, Martin Vogel","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-05-24T14:46:31Z","title":"General Toeplitz matrices subject to Gaussian perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10265","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fb212879f22f992dabaaa840d5cd8b4410f9844d6f46a1ef438ae92e2b3f6d95","target":"record","created_at":"2026-05-17T23:45:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7697a4cdcd0514a8aacc82f6a99fad697f865124fb1f770e0378ddce16bcd970","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-05-24T14:46:31Z","title_canon_sha256":"dfee211290e967fc1cf809c2b96c4f3531a27d7b31ecb1318b475da5358e9e36"},"schema_version":"1.0","source":{"id":"1905.10265","kind":"arxiv","version":1}},"canonical_sha256":"8b01b78084ac0038314558dd80afb77404dd4cddb2e94266a1092f24f7ade440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b01b78084ac0038314558dd80afb77404dd4cddb2e94266a1092f24f7ade440","first_computed_at":"2026-05-17T23:45:10.766111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:10.766111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VLXNG9Hniy/UNCXjyirGc9lKNUpBUFIlpa/bzAA+Gw/XL8OLuPrFRiEhZ02+sjQF98ElpP5uCDSeisHFpDuhAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:10.766843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb212879f22f992dabaaa840d5cd8b4410f9844d6f46a1ef438ae92e2b3f6d95","sha256:64b46cd758c4869a7c90add2aa72ae5c502af7fbc53276e7482151184ddef7cb"],"state_sha256":"e1c264d4df2499049223a81e550ea0141cf3abc4a4f413c4cfabd98fe65c0609"}