{"id":"W2537042157","doi":"10.1142/s2010326317500101","title":"Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles","year":2017,"lang":"en","type":"article","venue":"Random Matrices Theory and Application","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada; Fonds Québécois de la Recherche sur la Nature et les Technologies; Agence Nationale de la Recherche","keywords":"Universality (dynamical systems); Unitary state; Bessel function; Unitary matrix; Limiting; Circular ensemble; Limit (mathematics)","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":[0.0008732955,0.0001343656,0.0002961284,0.000053239,0.000712747,0.00003149975,0.0003002353,0.00007851283,0.00001301179],"category_scores_gemma":[0.000132893,0.00009429709,0.00009565774,0.0001198167,0.0004169256,0.0001500379,0.00017054,0.00008536602,0.000001883649],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001497677,"about_ca_system_score_gemma":0.00001891929,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008224536,"about_ca_topic_score_gemma":0.00004012054,"domain_scores_codex":[0.9990581,0.000143133,0.0003272455,0.0002132385,0.0001393295,0.00011894],"domain_scores_gemma":[0.9974597,0.001098177,0.0006370276,0.0006808168,0.00007754674,0.00004673197],"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":[0.001197307,0.0001750818,0.006839079,0.00060144,0.0001083597,2.42832e-7,0.0006693882,0.00001500747,0.01359728,0.9688706,0.0004405485,0.007485677],"study_design_scores_gemma":[0.007900105,0.00006829391,0.04411423,0.00011872,0.0009851591,0.00003065966,0.001747935,0.0004805997,0.03008286,0.9094902,0.00460677,0.0003744748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9825274,0.0009703296,0.01260982,0.0003976546,0.00003926985,0.0007026801,0.00007493484,0.00002911855,0.002648823],"genre_scores_gemma":[0.9978456,0.0006509648,0.0005084274,0.000007154182,0.00005839744,0.00004538809,0.000005945979,0.00001234876,0.0008657046],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0593804,"threshold_uncertainty_score":0.5481945,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01555667642997389,"score_gpt":0.2895083356952193,"score_spread":0.2739516592652454,"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."}}