{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:FIMJHHEHTIAUMYMTF3B655FVHZ","short_pith_number":"pith:FIMJHHEH","schema_version":"1.0","canonical_sha256":"2a18939c879a014661932ec3eef4b53e6fb69d445dd59aa2ebbc24d1a46af7fa","source":{"kind":"arxiv","id":"2307.08211","version":2},"attestation_state":"computed","paper":{"title":"On pseudospectrum of inhomogeneous non-Hermitian random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Konstantin Tikhomirov","submitted_at":"2023-07-17T03:01:35Z","abstract_excerpt":"Let $A$ be an $n\\times n$ matrix with mutually independent centered Gaussian entries. Define \\begin{align*} \\sigma^*:=\\max\\limits_{i,j\\leq n}\\sqrt{{\\mathbb E}\\,|A_{i,j}|^2}, \\quad \\sigma:=\\max\\bigg(\\max\\limits_{j\\leq n}\\sqrt{{\\mathbb E}\\,\\|{\\rm col}_j(A)\\|_2^2}, \\max\\limits_{i\\leq n}\\sqrt{{\\mathbb E}\\,\\|{\\rm row}_i(A)\\|_2^2}\\bigg). \\end{align*} Assume that $\\sigma\\geq n^\\varepsilon\\,\\sigma^*$ for a constant $\\varepsilon>0$, and that a complex number $z$ satisfies $|z|=\\Omega(\\sigma)$. We prove that $$ s_{\\min}(A-z\\,{\\rm Id}) \\geq |z|\\,\\exp\\bigg(-n^{o(1)}\\,\\Big(\\frac{\\sqrt{n}\\,\\sigma^*}{\\sigma}"},"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":"2307.08211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-17T03:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"8b7191a9eb3a09101c7181eb08ad5e801a9ee5b2b7aff46823b57a6337a6e0e9","abstract_canon_sha256":"425c589854d2156c8180e77d2365d9c625330f0fe4224b3538ae5b8daa4b2d73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:34:06.633874Z","signature_b64":"YWzksu6c41XIdz87Jg0kN19oaMLtPE05s/NbpNUWshVT0DsrRKZY43SZBmCSRqmDUF71ifF2j0XvFYgT2ck/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a18939c879a014661932ec3eef4b53e6fb69d445dd59aa2ebbc24d1a46af7fa","last_reissued_at":"2026-07-05T06:34:06.633470Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:34:06.633470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On pseudospectrum of inhomogeneous non-Hermitian random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Konstantin Tikhomirov","submitted_at":"2023-07-17T03:01:35Z","abstract_excerpt":"Let $A$ be an $n\\times n$ matrix with mutually independent centered Gaussian entries. Define \\begin{align*} \\sigma^*:=\\max\\limits_{i,j\\leq n}\\sqrt{{\\mathbb E}\\,|A_{i,j}|^2}, \\quad \\sigma:=\\max\\bigg(\\max\\limits_{j\\leq n}\\sqrt{{\\mathbb E}\\,\\|{\\rm col}_j(A)\\|_2^2}, \\max\\limits_{i\\leq n}\\sqrt{{\\mathbb E}\\,\\|{\\rm row}_i(A)\\|_2^2}\\bigg). \\end{align*} Assume that $\\sigma\\geq n^\\varepsilon\\,\\sigma^*$ for a constant $\\varepsilon>0$, and that a complex number $z$ satisfies $|z|=\\Omega(\\sigma)$. We prove that $$ s_{\\min}(A-z\\,{\\rm Id}) \\geq |z|\\,\\exp\\bigg(-n^{o(1)}\\,\\Big(\\frac{\\sqrt{n}\\,\\sigma^*}{\\sigma}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08211","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.08211/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2307.08211","created_at":"2026-07-05T06:34:06.633526+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.08211v2","created_at":"2026-07-05T06:34:06.633526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08211","created_at":"2026-07-05T06:34:06.633526+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIMJHHEHTIAU","created_at":"2026-07-05T06:34:06.633526+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIMJHHEHTIAUMYMT","created_at":"2026-07-05T06:34:06.633526+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIMJHHEH","created_at":"2026-07-05T06:34:06.633526+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01664","citing_title":"Brown measure convergence for the spectrum of polynomials in Ginibre matrices","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15355","citing_title":"Characteristic polynomials of non-Hermitian random band matrices near the threshold","ref_index":32,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ","json":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ.json","graph_json":"https://pith.science/api/pith-number/FIMJHHEHTIAUMYMTF3B655FVHZ/graph.json","events_json":"https://pith.science/api/pith-number/FIMJHHEHTIAUMYMTF3B655FVHZ/events.json","paper":"https://pith.science/paper/FIMJHHEH"},"agent_actions":{"view_html":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ","download_json":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ.json","view_paper":"https://pith.science/paper/FIMJHHEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.08211&json=true","fetch_graph":"https://pith.science/api/pith-number/FIMJHHEHTIAUMYMTF3B655FVHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/FIMJHHEHTIAUMYMTF3B655FVHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ/action/storage_attestation","attest_author":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ/action/author_attestation","sign_citation":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ/action/citation_signature","submit_replication":"https://pith.science/pith/FIMJHHEHTIAUMYMTF3B655FVHZ/action/replication_record"}},"created_at":"2026-07-05T06:34:06.633526+00:00","updated_at":"2026-07-05T06:34:06.633526+00:00"}