{"id":"W7132928073","doi":"","title":"A Mesoscopic Central Limit Theorem for Sample Covariance Matrices and their Linearization","year":2023,"lang":"","type":"dissertation","venue":"TSpace","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Central limit theorem; Limit (mathematics); Covariance; Covariance matrix; Random matrix; Linearization; Matrix (chemical analysis); Random variable","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005278138,0.001130642,0.001197584,0.002011331,0.0009750996,0.002132488,0.002352005,0.001470911,0.006243631],"category_scores_gemma":[0.02269167,0.0006613737,0.001645911,0.001494236,0.004230131,0.004915714,0.003161556,0.00377088,0.001534509],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002167515,"about_ca_system_score_gemma":0.001761522,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002613141,"about_ca_topic_score_gemma":0.001808481,"domain_scores_codex":[0.9982584,0.0006538439,0.00005446189,0.0003758986,0.0004804873,0.0001768624],"domain_scores_gemma":[0.9901632,0.005803868,0.0011149,0.0009112858,0.001559151,0.0004476143],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001815717,0.00002640643,0.0003570928,0.00008498863,0.00004312349,0.0001220289,0.0001579035,0.02041853,0.001713931,0.9705287,0.001656405,0.004872839],"study_design_scores_gemma":[0.00001475484,0.00004065706,0.0004003476,0.00004828081,0.00002298585,0.0001741405,0.00004708432,0.2733371,0.001501726,0.721801,0.0025658,0.00004605186],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01595419,0.0007185268,0.9695591,0.001394563,0.0001153248,0.00004248911,0.0001855565,0.0002513962,0.01177894],"genre_scores_gemma":[0.7351474,0.00258381,0.2240544,0.002834994,0.001070803,0.0006950513,0.0005761952,0.000761384,0.03227596],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006243631,"threshold_uncertainty_score":0.02791381,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04089980469410729,"score_gpt":0.3579093442812273,"score_spread":0.31700953958712,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}