{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BHPPNHKAW3WXKEALWWUGUBBY3J","short_pith_number":"pith:BHPPNHKA","schema_version":"1.0","canonical_sha256":"09def69d40b6ed75100bb5a86a0438da6b889e05646d53aac0fb65534689fe0b","source":{"kind":"arxiv","id":"1403.4593","version":1},"attestation_state":"computed","paper":{"title":"Universality of the ESD for a fixed matrix plus small random noise: a stability approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Matchett Wood","submitted_at":"2014-03-18T19:56:35Z","abstract_excerpt":"We study the empirical spectral distribution (ESD) in the limit where n goes to infinity of a fixed n by n matrix M_n plus small random noise of the form f(n)X_n, where X_n has iid mean 0, variance 1/n entries and f(n) goes to 0 as n goes to infinity. It is known for certain M_n, in the case where X_n is iid complex Gaussian, that the limiting distribution of the ESD of M_n+f(n)X_n can be dramatically different from that for M_n. We prove a general universality result showing, with some conditions on M_n and f(n), that the limiting distribution of the ESD does not depend on the type of distrib"},"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":"1403.4593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-18T19:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"0027013c69c32e0060fc0c51b79c7cdf48d64a2cad556c706a5c89ad9b0838a8","abstract_canon_sha256":"a872d33cd8c00c69f530ab2e89edb821e15cb1c679efe94166d2aa718e7bffdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:05.483362Z","signature_b64":"MLmT/3rYM7fGt1ejOSLDv6vYf0Lvl3Q3riA7VP6CXynC8oXPeEHSxrWfXHO85RZ44HgVtvzdrwZmaGexOLz6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09def69d40b6ed75100bb5a86a0438da6b889e05646d53aac0fb65534689fe0b","last_reissued_at":"2026-05-18T02:56:05.482890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:05.482890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality of the ESD for a fixed matrix plus small random noise: a stability approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Matchett Wood","submitted_at":"2014-03-18T19:56:35Z","abstract_excerpt":"We study the empirical spectral distribution (ESD) in the limit where n goes to infinity of a fixed n by n matrix M_n plus small random noise of the form f(n)X_n, where X_n has iid mean 0, variance 1/n entries and f(n) goes to 0 as n goes to infinity. It is known for certain M_n, in the case where X_n is iid complex Gaussian, that the limiting distribution of the ESD of M_n+f(n)X_n can be dramatically different from that for M_n. We prove a general universality result showing, with some conditions on M_n and f(n), that the limiting distribution of the ESD does not depend on the type of distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4593","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":"1403.4593","created_at":"2026-05-18T02:56:05.482958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.4593v1","created_at":"2026-05-18T02:56:05.482958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4593","created_at":"2026-05-18T02:56:05.482958+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHPPNHKAW3WX","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHPPNHKAW3WXKEAL","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHPPNHKA","created_at":"2026-05-18T12:28:22.404517+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/BHPPNHKAW3WXKEALWWUGUBBY3J","json":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J.json","graph_json":"https://pith.science/api/pith-number/BHPPNHKAW3WXKEALWWUGUBBY3J/graph.json","events_json":"https://pith.science/api/pith-number/BHPPNHKAW3WXKEALWWUGUBBY3J/events.json","paper":"https://pith.science/paper/BHPPNHKA"},"agent_actions":{"view_html":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J","download_json":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J.json","view_paper":"https://pith.science/paper/BHPPNHKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.4593&json=true","fetch_graph":"https://pith.science/api/pith-number/BHPPNHKAW3WXKEALWWUGUBBY3J/graph.json","fetch_events":"https://pith.science/api/pith-number/BHPPNHKAW3WXKEALWWUGUBBY3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J/action/storage_attestation","attest_author":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J/action/author_attestation","sign_citation":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J/action/citation_signature","submit_replication":"https://pith.science/pith/BHPPNHKAW3WXKEALWWUGUBBY3J/action/replication_record"}},"created_at":"2026-05-18T02:56:05.482958+00:00","updated_at":"2026-05-18T02:56:05.482958+00:00"}