{"id":"W2963503596","doi":"10.1017/apr.2019.10","title":"Singular vector distribution of sample covariance matrices","year":2019,"lang":"en","type":"article","venue":"Advances in Applied Probability","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Independent and identically distributed random variables; Singular value; Random matrix; Gaussian; Covariance matrix; Multivariate random variable; Sample mean and sample covariance; Covariance; Circular law","routes":{"ca_aff":true,"ca_fund":false,"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":[0.004470924,0.0006284551,0.001128568,0.001948094,0.0006443467,0.001714226,0.00132324,0.001109134,0.003105179],"category_scores_gemma":[0.02085633,0.0004406743,0.0007236949,0.0008417399,0.003756807,0.002199011,0.001090203,0.001415279,0.0005574586],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001085898,"about_ca_system_score_gemma":0.0008560707,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002133498,"about_ca_topic_score_gemma":0.001101598,"domain_scores_codex":[0.9978133,0.0005987073,0.00007642594,0.000583151,0.0006324321,0.0002958005],"domain_scores_gemma":[0.9869131,0.006837829,0.001443761,0.001898072,0.002366562,0.0005406538],"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":[0.0002887114,0.0001256031,0.008149415,0.0001564353,0.0001833603,0.0005155444,0.0002612573,0.2695183,0.01223286,0.6852621,0.00273483,0.02057152],"study_design_scores_gemma":[0.00002093814,0.00005003389,0.003046523,0.00002452279,0.0000166588,0.0001666078,0.00004728502,0.8506525,0.002424781,0.1426381,0.0008643296,0.00004764588],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1934735,0.0003098766,0.8013651,0.000359809,0.00006074479,0.0000808858,0.0002992437,0.0004751579,0.003575562],"genre_scores_gemma":[0.9619541,0.0002845653,0.03392645,0.0001169978,0.0001472926,0.0001113443,0.0006802691,0.0001255321,0.002653501],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004470924,"threshold_uncertainty_score":0.0236448,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01672069056819517,"score_gpt":0.2943323347918342,"score_spread":0.277611644223639,"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."}}