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It is shown that the empirical spectral distribution of the quaternion sample covariance matrix $\\mathbf S_n=n^{-1}\\mathbf X_n\\mathbf X_n^*$ converges to the M-P law as $p\\to\\infty$, $n\\to\\infty$ and $p/n\\to y\\in(0,+\\infty)$."},"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":"1310.5428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T05:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"5c8fa8fc98fe361a4d930f8d4809883a4f5104de0bd95fc1a85e76e1155644b9","abstract_canon_sha256":"2637fdf95206eca4917c0209d7f1ea5bc81361fb79c1b2b2425f5650386832fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:35.793235Z","signature_b64":"NPje7O15oxcMzxQQqsKSVjpRjYM8YYLIKlzYBm4cdKWoT8bLIY9XJmL74kELAWMRYo1KS1OJ2LF1Pb9T1s/CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a57a52f765880cea387cbd0132584b22a1703841b1e9bac5d78a143575ef1b24","last_reissued_at":"2026-05-18T03:09:35.792473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:35.792473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of Empirical Spectral Distributions of Large Dimensional Quaternion Sample Covariance Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huiqin Li, Jiang Hu, Zhidong Bai","submitted_at":"2013-10-21T05:21:48Z","abstract_excerpt":"In this paper we establish the limit of the empirical spectral distribution of quaternion sample covariance matrices. 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