{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WRT7HWGKJMGSORKO5J74ERHD4W","short_pith_number":"pith:WRT7HWGK","schema_version":"1.0","canonical_sha256":"b467f3d8ca4b0d27454eea7fc244e3e5a849b167cc20207f0bdecd0c5d9a64cf","source":{"kind":"arxiv","id":"1801.02111","version":1},"attestation_state":"computed","paper":{"title":"Convergence of the empirical spectral distribution of Gaussian matrix-valued processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, Jos\\'e Luis P\\'erez, Juan Carlos Pardo","submitted_at":"2018-01-07T01:52:14Z","abstract_excerpt":"For a given normalized Gaussian symmetric matrix-valued process $Y^{(n)}$, we consider the process of its eigenvalues $\\{(\\lambda_{1}^{(n)}(t),\\dots, \\lambda_{n}^{(n)}(t)); t\\ge 0\\}$ as well as its corresponding process of empirical spectral measures $\\mu^{(n)}=(\\mu_{t}^{(n)}; t\\geq0)$. Under some mild conditions on the covariance function associated to $Y^{(n)}$, we prove that the process $\\mu^{(n)}$ converges in probability to a deterministic limit $\\mu$, in the topology of uniform convergence over compact sets. We show that the process $\\mu$ is characterized by its Cauchy transform, which i"},"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":"1801.02111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-07T01:52:14Z","cross_cats_sorted":[],"title_canon_sha256":"bb82d71a23e7caa3889a2173d4d0d3cb656b5e48cf198bbc9a98c84633aecb2e","abstract_canon_sha256":"f4c13e5bf1674fe1e07b46e98bf6f0b5c3ddf49c99e838abd2af6ebbd1fab3aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:34.858199Z","signature_b64":"Ug8si/Mf4a1mv8peQ79k6rnjZjF9qNP+JN0a/Y8DRh/1PRy1waehzdAaFJKIjp67TFc9D19pJXqW9PNGVh0nDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b467f3d8ca4b0d27454eea7fc244e3e5a849b167cc20207f0bdecd0c5d9a64cf","last_reissued_at":"2026-05-18T00:26:34.857520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:34.857520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of the empirical spectral distribution of Gaussian matrix-valued processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, Jos\\'e Luis P\\'erez, Juan Carlos Pardo","submitted_at":"2018-01-07T01:52:14Z","abstract_excerpt":"For a given normalized Gaussian symmetric matrix-valued process $Y^{(n)}$, we consider the process of its eigenvalues $\\{(\\lambda_{1}^{(n)}(t),\\dots, \\lambda_{n}^{(n)}(t)); t\\ge 0\\}$ as well as its corresponding process of empirical spectral measures $\\mu^{(n)}=(\\mu_{t}^{(n)}; t\\geq0)$. Under some mild conditions on the covariance function associated to $Y^{(n)}$, we prove that the process $\\mu^{(n)}$ converges in probability to a deterministic limit $\\mu$, in the topology of uniform convergence over compact sets. We show that the process $\\mu$ is characterized by its Cauchy transform, which i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02111","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":"1801.02111","created_at":"2026-05-18T00:26:34.857645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.02111v1","created_at":"2026-05-18T00:26:34.857645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02111","created_at":"2026-05-18T00:26:34.857645+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRT7HWGKJMGS","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRT7HWGKJMGSORKO","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRT7HWGK","created_at":"2026-05-18T12:33:01.666342+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/WRT7HWGKJMGSORKO5J74ERHD4W","json":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W.json","graph_json":"https://pith.science/api/pith-number/WRT7HWGKJMGSORKO5J74ERHD4W/graph.json","events_json":"https://pith.science/api/pith-number/WRT7HWGKJMGSORKO5J74ERHD4W/events.json","paper":"https://pith.science/paper/WRT7HWGK"},"agent_actions":{"view_html":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W","download_json":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W.json","view_paper":"https://pith.science/paper/WRT7HWGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.02111&json=true","fetch_graph":"https://pith.science/api/pith-number/WRT7HWGKJMGSORKO5J74ERHD4W/graph.json","fetch_events":"https://pith.science/api/pith-number/WRT7HWGKJMGSORKO5J74ERHD4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W/action/storage_attestation","attest_author":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W/action/author_attestation","sign_citation":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W/action/citation_signature","submit_replication":"https://pith.science/pith/WRT7HWGKJMGSORKO5J74ERHD4W/action/replication_record"}},"created_at":"2026-05-18T00:26:34.857645+00:00","updated_at":"2026-05-18T00:26:34.857645+00:00"}