{"paper":{"title":"Largest Eigenvalues of Principal Minors of Deformed Gaussian Orthogonal Ensembles and Wishart Matrices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tiefeng Jiang, Yongcheng Qi","submitted_at":"2024-10-19T17:17:21Z","abstract_excerpt":"Consider a high-dimensional Wishart matrix $\\bd{W}=\\bd{X}^T\\bd{X}$ where the entries of $\\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\\eta$. Motivated by problems in signal processing and high-dimensional statistics, we study the maximum of the largest eigenvalues of any two-by-two principal minors of $\\bd{W}$. Under certain restrictions on the sample size and the population dimension of $\\bd{W}$, we obtain the limiting distribution of the maximum, which follows the Gumbel distribution when $\\eta$ is between 0 and 3, and a new distribution when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.15160","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.15160/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}