{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HLEYQMZCULUYJPCLUSKHIU775Z","short_pith_number":"pith:HLEYQMZC","schema_version":"1.0","canonical_sha256":"3ac9883322a2e984bc4ba4947453ffee5d49f641c087c0c9b92f53203aa9d8cd","source":{"kind":"arxiv","id":"1602.08613","version":2},"attestation_state":"computed","paper":{"title":"CLT for linear eigenvalue statistics for a tensor product version of sample covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Lytova","submitted_at":"2016-02-27T17:12:35Z","abstract_excerpt":"For $k,m,n\\in \\mathbb{N}$, we consider $n^k\\times n^k$ random matrices of the form $$ \\mathcal{M}_{n,m,k}(\\mathbf{y})=\\sum_{\\alpha=1}^m\\tau_\\alpha {Y_\\alpha}Y_\\alpha^T,\\quad Y_\\alpha=\\mathbf{y}_\\alpha^{(1)}\\otimes...\\otimes\\mathbf{y}_\\alpha^{(k)}, $$ where $\\tau _{\\alpha }$, $\\alpha\\in[m]$, are real numbers and $\\mathbf{y}_\\alpha^{(j)}$, $\\alpha\\in[m]$, $j\\in[k]$, are i.i.d. copies of a normalized isotropic random vector $\\mathbf{y}\\in \\mathbb{R}^n$. For every fixed $k\\ge 1$, if the Normalized Counting Measures of $\\{\\tau _{\\alpha }\\}_{\\alpha}$ converge weakly as $m,n\\rightarrow \\infty$, $m/n^"},"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":"1602.08613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-27T17:12:35Z","cross_cats_sorted":[],"title_canon_sha256":"4dae07bc240a6cbc39bdba431429118e34d0c566ebd20357afb73076f7b1f197","abstract_canon_sha256":"0ca527292e3f3859b0ca397b600a440de95d494b67c7fc6b69aa6e724e291a93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.122214Z","signature_b64":"Hni8dBoYZ/pot3G7GkQ7QFQf4wXiWSiJCaiR5O4kL82pMGKY2ZJmYKYVMxB20vw3RUNWbgXW4xakHEbkHQA6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ac9883322a2e984bc4ba4947453ffee5d49f641c087c0c9b92f53203aa9d8cd","last_reissued_at":"2026-05-18T00:52:04.121487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.121487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CLT for linear eigenvalue statistics for a tensor product version of sample covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Lytova","submitted_at":"2016-02-27T17:12:35Z","abstract_excerpt":"For $k,m,n\\in \\mathbb{N}$, we consider $n^k\\times n^k$ random matrices of the form $$ \\mathcal{M}_{n,m,k}(\\mathbf{y})=\\sum_{\\alpha=1}^m\\tau_\\alpha {Y_\\alpha}Y_\\alpha^T,\\quad Y_\\alpha=\\mathbf{y}_\\alpha^{(1)}\\otimes...\\otimes\\mathbf{y}_\\alpha^{(k)}, $$ where $\\tau _{\\alpha }$, $\\alpha\\in[m]$, are real numbers and $\\mathbf{y}_\\alpha^{(j)}$, $\\alpha\\in[m]$, $j\\in[k]$, are i.i.d. copies of a normalized isotropic random vector $\\mathbf{y}\\in \\mathbb{R}^n$. For every fixed $k\\ge 1$, if the Normalized Counting Measures of $\\{\\tau _{\\alpha }\\}_{\\alpha}$ converge weakly as $m,n\\rightarrow \\infty$, $m/n^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08613","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":""},"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":"1602.08613","created_at":"2026-05-18T00:52:04.121601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.08613v2","created_at":"2026-05-18T00:52:04.121601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08613","created_at":"2026-05-18T00:52:04.121601+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLEYQMZCULUY","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLEYQMZCULUYJPCL","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLEYQMZC","created_at":"2026-05-18T12:30:19.053100+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/HLEYQMZCULUYJPCLUSKHIU775Z","json":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z.json","graph_json":"https://pith.science/api/pith-number/HLEYQMZCULUYJPCLUSKHIU775Z/graph.json","events_json":"https://pith.science/api/pith-number/HLEYQMZCULUYJPCLUSKHIU775Z/events.json","paper":"https://pith.science/paper/HLEYQMZC"},"agent_actions":{"view_html":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z","download_json":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z.json","view_paper":"https://pith.science/paper/HLEYQMZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.08613&json=true","fetch_graph":"https://pith.science/api/pith-number/HLEYQMZCULUYJPCLUSKHIU775Z/graph.json","fetch_events":"https://pith.science/api/pith-number/HLEYQMZCULUYJPCLUSKHIU775Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z/action/storage_attestation","attest_author":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z/action/author_attestation","sign_citation":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z/action/citation_signature","submit_replication":"https://pith.science/pith/HLEYQMZCULUYJPCLUSKHIU775Z/action/replication_record"}},"created_at":"2026-05-18T00:52:04.121601+00:00","updated_at":"2026-05-18T00:52:04.121601+00:00"}