{"id":"W4387010240","doi":"10.1007/s00440-023-01230-8","title":"Local law and rigidity for unitary Brownian motion","year":2023,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Directorate for Mathematical and Physical Sciences","keywords":"Mathematics; Brownian motion; Measure (data warehouse); Mathematical analysis; Unitary state; Eigenvalues and eigenvectors; Unitary matrix; Unit circle; Probability measure; Quantum mechanics; Law; Statistics; Physics","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":[0.00120519,0.00008172455,0.0001303514,0.00002486678,0.0002152154,0.00001916733,0.00005142828,0.0002077542,0.00002747205],"category_scores_gemma":[0.0001710874,0.00006365382,0.00004390589,0.0001325891,0.0001816389,0.0000652867,0.00003955388,0.0001627357,0.000007156987],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007401431,"about_ca_system_score_gemma":0.000006621263,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001494601,"about_ca_topic_score_gemma":0.00002029971,"domain_scores_codex":[0.9993418,0.0001056595,0.0001839267,0.0001922199,0.00004793787,0.0001284239],"domain_scores_gemma":[0.9985772,0.001122574,0.00004057192,0.0001746323,0.00003296285,0.00005206708],"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":[0.00007224853,0.00004341857,0.00004014674,0.0001932787,0.00002234752,4.682345e-7,0.0004499345,0.00001851426,0.00001445522,0.9948185,0.0002434928,0.004083186],"study_design_scores_gemma":[0.0005260336,0.00004430863,0.0001766019,0.00001416108,0.00004886389,0.000006318064,0.0001533596,0.001950414,0.000113627,0.9956064,0.001278624,0.0000812807],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9202595,0.0001775553,0.06478019,0.002494439,0.0001170613,0.001228189,0.00003306949,0.0003296358,0.01058031],"genre_scores_gemma":[0.9984364,0.00006747815,0.000736583,0.00008216703,0.00001958002,0.0000581504,0.00001526346,0.000008523496,0.0005758655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07817684,"threshold_uncertainty_score":0.2595727,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02895369825124109,"score_gpt":0.2872726531587823,"score_spread":0.2583189549075411,"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."}}