{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZCBURDMCULGSSPXMWDWNVK2ZE7","short_pith_number":"pith:ZCBURDMC","schema_version":"1.0","canonical_sha256":"c883488d82a2cd293eecb0ecdaab5927c3c3b45f3e25ee3e1ffc0c2fa6019f5d","source":{"kind":"arxiv","id":"1908.08150","version":3},"attestation_state":"computed","paper":{"title":"Brown Measures of Free Circular and Multiplicative Brownian Motions with Self-Adjoint and Unitary Initial Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Ching-Wei Ho, Ping Zhong","submitted_at":"2019-08-22T00:14:58Z","abstract_excerpt":"Let $Z_N$ be a Ginibre ensemble and let $A_N$ be a Hermitian random matrix independent from $Z_N$ such that $A_N$ converges in distribution to a self-adjoint random variable $x_0$. For each $t>0$, the random matrix $A_N+\\sqrt{t}Z_N$ converges in $\\ast$-distribution to $x_0+c_t$, where $c_t$ is the circular variable of variance $t$, free from $x_0$. We use the Hamilton-Jacobi method to compute the Brown measure $\\rho_t$ of $x_0+c_t$. The Brown measure has a density that is constant along the vertical direction inside the support. The support of the Brown measure of $x_0+c_t$ is related to the s"},"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":"1908.08150","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-08-22T00:14:58Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"title_canon_sha256":"b9ee5933157cd3e801160bf374e50a94bca725e810a7bed6db48b619c4966b44","abstract_canon_sha256":"99533dbd4a6dc05c3e82e32f8ab79128d78136a73b93409526b5dcbf8186109c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:23.490517Z","signature_b64":"xlc3EDY02IGDKDV25PxOvLtgSJysFu6QeyKVfkVCu6J8yw2ZYj5Rw/2zLLGtK+5U+Wz1j83dOGQBG0qltdY/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c883488d82a2cd293eecb0ecdaab5927c3c3b45f3e25ee3e1ffc0c2fa6019f5d","last_reissued_at":"2026-07-05T03:18:23.490130Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:23.490130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brown Measures of Free Circular and Multiplicative Brownian Motions with Self-Adjoint and Unitary Initial Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Ching-Wei Ho, Ping Zhong","submitted_at":"2019-08-22T00:14:58Z","abstract_excerpt":"Let $Z_N$ be a Ginibre ensemble and let $A_N$ be a Hermitian random matrix independent from $Z_N$ such that $A_N$ converges in distribution to a self-adjoint random variable $x_0$. For each $t>0$, the random matrix $A_N+\\sqrt{t}Z_N$ converges in $\\ast$-distribution to $x_0+c_t$, where $c_t$ is the circular variable of variance $t$, free from $x_0$. We use the Hamilton-Jacobi method to compute the Brown measure $\\rho_t$ of $x_0+c_t$. The Brown measure has a density that is constant along the vertical direction inside the support. The support of the Brown measure of $x_0+c_t$ is related to the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08150","kind":"arxiv","version":3},"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/1908.08150/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":"1908.08150","created_at":"2026-07-05T03:18:23.490191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08150v3","created_at":"2026-07-05T03:18:23.490191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08150","created_at":"2026-07-05T03:18:23.490191+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZCBURDMCULGS","created_at":"2026-07-05T03:18:23.490191+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZCBURDMCULGSSPXM","created_at":"2026-07-05T03:18:23.490191+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZCBURDMC","created_at":"2026-07-05T03:18:23.490191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13922","citing_title":"Strong Convergence of Multiplicative Brownian Motions on the General Linear Group","ref_index":46,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7","json":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7.json","graph_json":"https://pith.science/api/pith-number/ZCBURDMCULGSSPXMWDWNVK2ZE7/graph.json","events_json":"https://pith.science/api/pith-number/ZCBURDMCULGSSPXMWDWNVK2ZE7/events.json","paper":"https://pith.science/paper/ZCBURDMC"},"agent_actions":{"view_html":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7","download_json":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7.json","view_paper":"https://pith.science/paper/ZCBURDMC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08150&json=true","fetch_graph":"https://pith.science/api/pith-number/ZCBURDMCULGSSPXMWDWNVK2ZE7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZCBURDMCULGSSPXMWDWNVK2ZE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7/action/storage_attestation","attest_author":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7/action/author_attestation","sign_citation":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7/action/citation_signature","submit_replication":"https://pith.science/pith/ZCBURDMCULGSSPXMWDWNVK2ZE7/action/replication_record"}},"created_at":"2026-07-05T03:18:23.490191+00:00","updated_at":"2026-07-05T03:18:23.490191+00:00"}