{"id":"W3084237930","doi":"","title":"Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes","year":2012,"lang":"en","type":"article","venue":"Spectrum Research Repository (Concordia University)","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Concordia University","funders":"","keywords":"Hermitian matrix; Spectral line; Rank (graph theory); Critical phenomena; Mathematics; Physics; Statistical physics; Condensed matter physics; Pure mathematics; Combinatorics; Quantum mechanics; Phase transition","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001024065,0.0001929586,0.000360724,0.0002360387,0.0009695874,0.0001928385,0.0004971655,0.0001092596,0.00005643203],"category_scores_gemma":[0.000365754,0.000139632,0.0001304175,0.0007203061,0.001773146,0.0003079106,0.0002017087,0.0006009556,0.000008986176],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000886436,"about_ca_system_score_gemma":0.0001953587,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001703741,"about_ca_topic_score_gemma":0.0002757019,"domain_scores_codex":[0.9974977,0.0005733663,0.0002629056,0.0003337043,0.0005875808,0.0007446914],"domain_scores_gemma":[0.9944171,0.004375774,0.00009289119,0.0005520123,0.0001907,0.0003714842],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"observational","study_design_scores_codex":[0.003474389,0.0009686622,0.1158242,0.0008720499,0.0003474825,0.0004412394,0.003304289,0.000006175447,0.004563895,0.8672008,0.001555504,0.001441342],"study_design_scores_gemma":[0.04391436,0.005970854,0.3147618,0.002516356,0.00447559,0.007568173,0.05384636,0.004140185,0.09672748,0.2073964,0.2536296,0.005052866],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9559691,0.000924874,0.007940189,0.002546199,0.00008544026,0.0005703776,0.00000707569,0.00007449055,0.03188225],"genre_scores_gemma":[0.9944,0.0001184499,0.002173898,0.000008981124,0.0003475128,0.000006608949,5.383537e-7,0.00003016877,0.002913866],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6598044,"threshold_uncertainty_score":0.7457381,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03984087480340211,"score_gpt":0.3098627701698384,"score_spread":0.2700218953664363,"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."}}