{"id":"W3140827421","doi":"10.1002/rsa.70030","title":"Sampling Matrices From Harish‐Chandra–Itzykson–Zuber Densities With Applications to Quantum Inference and Differential Privacy","year":2025,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Japan Science and Technology Agency; Deutsche Forschungsgemeinschaft; National Science Foundation; National Science and Technology Council","keywords":"Lambda; Hermitian matrix; Random matrix; Haar measure; Unitary matrix; Eigenvalues and eigenvectors; Distribution (mathematics); Matrix (chemical analysis); Combinatorics; Mathematics; Discrete mathematics; Physics; Unitary state; Pure mathematics; Quantum mechanics; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003738115,0.0008556402,0.001103937,0.00125619,0.0009574673,0.0015611,0.001861794,0.001083939,0.002385786],"category_scores_gemma":[0.02566614,0.0006068462,0.0007547131,0.001416371,0.003010054,0.003800629,0.003200755,0.002675626,0.000433086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00187652,"about_ca_system_score_gemma":0.001394356,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001695783,"about_ca_topic_score_gemma":0.001753035,"domain_scores_codex":[0.9973025,0.00134732,0.00009333793,0.0003992816,0.0006616989,0.0001957986],"domain_scores_gemma":[0.9865392,0.009967193,0.0007888891,0.001519245,0.0007568047,0.0004287259],"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":[0.0005168021,0.0001590423,0.001948158,0.000128974,0.00007343509,0.0001522419,0.000343389,0.3420553,0.005283058,0.5944212,0.002015771,0.05290269],"study_design_scores_gemma":[0.00003697777,0.00003982754,0.0002377516,0.00001435474,0.000006700501,0.00004784736,0.00002550005,0.8202463,0.003013653,0.1757616,0.0005498987,0.00001970984],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04805242,0.0001869542,0.9491808,0.0005216438,0.00003323356,0.00007489349,0.00009383335,0.0003352894,0.001520925],"genre_scores_gemma":[0.6448954,0.0003230475,0.3500377,0.0003919649,0.0001104698,0.0002933596,0.0003734684,0.0001787717,0.00339581],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003738115,"threshold_uncertainty_score":0.01976931,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02520053893936581,"score_gpt":0.3218748276282398,"score_spread":0.296674288688874,"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."}}