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Assume that the entries of $\\mathbf X_n$ ($p\\times n$) are independent quaternion random variables with mean zero, variance 1 and uniformly bounded sixth moments. Denote $\\mathbf S_n=\\frac{1}{n}\\mathbf X_n\\mathbf X_n^*$. Using Bai inequality, we prove that the expected empirical spectral distribution (ESD) converges to the limiting Mar${\\rm \\check{c}}$enko-Pastur distribution with the ratio of the dimension to sample size $y_p=p/n$ at a rate of $O\\left(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":"1312.6926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-25T05:13:15Z","cross_cats_sorted":[],"title_canon_sha256":"840b321d49d332709210f1ed4649a9103239b6cfab71c3bd1b9c7e13b05305f2","abstract_canon_sha256":"8e93e45aa8aff3fd37460f63dd64abe0436d07022292ac314feedb5f10f12d2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:46.446997Z","signature_b64":"GoD7QZGQWP1pZKOvUiTPcxNqC9CLv/jKg7XYoRzunjkdATfROzFYLPxKPrAx0WseSDBk6YLefecf33lFZEg/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf1d6b7b88dc91b5a1238d2388084c72feb9b431eb333a40be6847451826da68","last_reissued_at":"2026-05-18T03:03:46.446247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:46.446247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Rates of Spectral Distribution of Large Dimensional Quaternion Sample Covariance Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huiqin Li, Zhidong Bai","submitted_at":"2013-12-25T05:13:15Z","abstract_excerpt":"In this paper, we study the convergence rates of empirical spectral distribution of large dimensional quaternion sample covariance matrix. 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