{"paper":{"title":"Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Baisuo Jin, Chen Wang, K. Krishnan Nair, Matthew Harding, Z. D. Bai","submitted_at":"2013-12-08T22:55:01Z","abstract_excerpt":"The auto-cross covariance matrix is defined as \\[\\mathbf{M}_n=\\frac{1} {2T}\\sum_{j=1}^T\\bigl(\\mathbf{e}_j\\mathbf{e}_{j+\\tau}^*+\\mathbf{e}_{j+ \\tau}\\mathbf{e}_j^*\\bigr),\\] where $\\mathbf{e}_j$'s are $n$-dimensional vectors of independent standard complex components with a common mean 0, variance $\\sigma^2$, and uniformly bounded $2+\\eta$th moments and $\\tau$ is the lag. Jin et al. [Ann. Appl. Probab. 24 (2014) 1199-1225] has proved that the LSD of $\\mathbf{M}_n$ exists uniquely and nonrandomly, and independent of $\\tau$ for all $\\tau\\ge 1$. And in addition they gave an analytic expression of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2277","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"}