{"id":"W2124636303","doi":"10.1007/s00440-017-0778-9","title":"On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence","year":2017,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Institut Universitaire de France; University of Alberta","keywords":"Mathematics; Multivariate random variable; Random matrix; Eigenvalues and eigenvectors; Covariance; Rank (graph theory); Covariance matrix; Estimation of covariance matrices; Dimension (graph theory); Applied mathematics; Combinatorics; Random variable; Statistics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001243854,0.00008602549,0.0001653373,0.000009324728,0.0003343147,0.00001936977,0.0004452401,0.0001219721,0.0001129951],"category_scores_gemma":[0.0009292982,0.00003717507,0.00006218226,0.0000758621,0.0006026842,0.00005602825,0.00009027556,0.0002346501,0.000001679117],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000004313132,"about_ca_system_score_gemma":0.0000313871,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000150045,"about_ca_topic_score_gemma":0.000009844646,"domain_scores_codex":[0.9991431,0.0002111754,0.0002443814,0.0001598373,0.0001504943,0.00009102075],"domain_scores_gemma":[0.9968863,0.001893439,0.0003490356,0.0007827631,0.00006719925,0.00002125735],"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":[0.0002283555,0.0001030325,0.00503553,0.0001157475,0.00004284003,3.700827e-7,0.0008407602,0.00003657384,0.00006854892,0.9931927,0.00005918715,0.0002762974],"study_design_scores_gemma":[0.000270067,0.00006571665,0.005582295,0.00009140385,0.00006579154,0.000006437748,0.0001104567,0.0002339165,0.002320564,0.9911728,0.000022326,0.00005820874],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9896613,0.00015429,0.002531466,0.00182103,0.00004965155,0.0004689996,0.000006172753,0.00001158504,0.005295504],"genre_scores_gemma":[0.9990622,0.0000704342,0.0004890217,0.00003097081,0.000006954902,0.00001675776,1.237862e-7,0.000004411145,0.0003191216],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009400903,"threshold_uncertainty_score":0.2571312,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04414027607880584,"score_gpt":0.3179711193613077,"score_spread":0.2738308432825018,"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."}}