{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2PYNECBR6MU5MZW5LFQC7KIMV4","short_pith_number":"pith:2PYNECBR","schema_version":"1.0","canonical_sha256":"d3f0d20831f329d666dd59602fa90caf3f690d322b4a2e3114a6db15415cc2eb","source":{"kind":"arxiv","id":"1906.10674","version":1},"attestation_state":"computed","paper":{"title":"Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charles Bordenave, Guillaume C\\'ebron, Mireille Capitaine, Serban Belinschi","submitted_at":"2019-06-25T17:24:47Z","abstract_excerpt":"We consider a square random matrix of size $N$ of the form $P(Y,A)$ where $P$ is a noncommutative polynomial, $A$ is a tuple of deterministic matrices converging in $\\ast$-distribution, when $N$ goes to infinity, towards a tuple $a$ in some $\\mathcal{C}^*$-probability space and $Y$ is a tuple of independent matrices with i.i.d. centered entries with variance $1/N$. We investigate the eigenvalues of $P(Y,A)$ outside the spectrum of $P(c,a)$ where $c$ is a circular system which is free from $a$. We provide a sufficient condition to guarantee that these eigenvalues coincide asymptotically with th"},"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":"1906.10674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-25T17:24:47Z","cross_cats_sorted":[],"title_canon_sha256":"e007d8586b8f2e42bde422e0684003ca4fd6e01e867d9b62e5d2d98352260861","abstract_canon_sha256":"7466662923c526e5088dd1ac4f3315d7375256adab835024520d41335fdaf288"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:15.628413Z","signature_b64":"6ulHAZej/GWSvF5gyL+WXsUZijGlL5ooCPi9sZQzTQRNwCtTofUcEQPYGQQROW7+KAbx0uN+vtaApadV5+OrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3f0d20831f329d666dd59602fa90caf3f690d322b4a2e3114a6db15415cc2eb","last_reissued_at":"2026-05-17T23:42:15.627827Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:15.627827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charles Bordenave, Guillaume C\\'ebron, Mireille Capitaine, Serban Belinschi","submitted_at":"2019-06-25T17:24:47Z","abstract_excerpt":"We consider a square random matrix of size $N$ of the form $P(Y,A)$ where $P$ is a noncommutative polynomial, $A$ is a tuple of deterministic matrices converging in $\\ast$-distribution, when $N$ goes to infinity, towards a tuple $a$ in some $\\mathcal{C}^*$-probability space and $Y$ is a tuple of independent matrices with i.i.d. centered entries with variance $1/N$. We investigate the eigenvalues of $P(Y,A)$ outside the spectrum of $P(c,a)$ where $c$ is a circular system which is free from $a$. We provide a sufficient condition to guarantee that these eigenvalues coincide asymptotically with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10674","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":"1906.10674","created_at":"2026-05-17T23:42:15.627909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10674v1","created_at":"2026-05-17T23:42:15.627909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10674","created_at":"2026-05-17T23:42:15.627909+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PYNECBR6MU5","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PYNECBR6MU5MZW5","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PYNECBR","created_at":"2026-05-18T12:33:07.085635+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/2PYNECBR6MU5MZW5LFQC7KIMV4","json":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4.json","graph_json":"https://pith.science/api/pith-number/2PYNECBR6MU5MZW5LFQC7KIMV4/graph.json","events_json":"https://pith.science/api/pith-number/2PYNECBR6MU5MZW5LFQC7KIMV4/events.json","paper":"https://pith.science/paper/2PYNECBR"},"agent_actions":{"view_html":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4","download_json":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4.json","view_paper":"https://pith.science/paper/2PYNECBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10674&json=true","fetch_graph":"https://pith.science/api/pith-number/2PYNECBR6MU5MZW5LFQC7KIMV4/graph.json","fetch_events":"https://pith.science/api/pith-number/2PYNECBR6MU5MZW5LFQC7KIMV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4/action/storage_attestation","attest_author":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4/action/author_attestation","sign_citation":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4/action/citation_signature","submit_replication":"https://pith.science/pith/2PYNECBR6MU5MZW5LFQC7KIMV4/action/replication_record"}},"created_at":"2026-05-17T23:42:15.627909+00:00","updated_at":"2026-05-17T23:42:15.627909+00:00"}