{"id":"W2099864191","doi":"10.48550/arxiv.1204.5154","title":"Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed\\n or localized vectors","year":2012,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Agence Nationale de la Recherche; York University; New York University Abu Dhabi","keywords":"Bijection, injection and surjection; Mathematics; Combinatorics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001884933,0.001100933,0.0009501961,0.003326991,0.001493622,0.003048815,0.001387984,0.001573531,0.008910979],"category_scores_gemma":[0.01172737,0.000629015,0.00105042,0.002249629,0.004289324,0.005498187,0.002287444,0.003406348,0.002157807],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002313375,"about_ca_system_score_gemma":0.0009101675,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002104783,"about_ca_topic_score_gemma":0.001088532,"domain_scores_codex":[0.9988953,0.0003452193,0.00003330665,0.0002723744,0.0003032855,0.0001504045],"domain_scores_gemma":[0.9965564,0.001512692,0.0005100526,0.0004942726,0.0005654421,0.0003611972],"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":[0.000007905776,0.00000689042,0.000116709,0.00002034835,0.000003836238,0.00001927809,0.00005245488,0.0009729164,0.0001903659,0.9946427,0.0009119918,0.003054542],"study_design_scores_gemma":[0.00001098672,0.00001434508,0.000390758,0.00001864646,0.000004881013,0.0001282827,0.00003753148,0.02347292,0.0003308913,0.9700009,0.005568678,0.00002126631],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1703811,0.00897311,0.7020109,0.006420659,0.0008433401,0.0001117948,0.0009025515,0.0005033687,0.1098533],"genre_scores_gemma":[0.8679599,0.007489999,0.06151693,0.001292762,0.001819431,0.0003853255,0.0008787979,0.0004657528,0.05819103],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008910979,"threshold_uncertainty_score":0.02981019,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1410870980623821,"score_gpt":0.2477582640401384,"score_spread":0.1066711659777563,"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."}}