{"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. Suppose $\\mathbf X_n = ({x_{jk}^{(n)}})_{p\\times n}$ is a quaternion random matrix. For each $n$, the entries $\\{x_{ij}^{(n)}\\}$ are independent random quaternion variables with a common mean $\\mu$ and variance $\\sigma^2>0$. 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 $p/n\\to y\\in(0,+\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5428","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"}