{"id":"W2332899829","doi":"10.4153/cmb-2006-039-7","title":"A Free Logarithmic Sobolev Inequality on the Circle","year":2006,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; Hungarian Scientific Research Fund; Canadian Mathematical Society","keywords":"Mathematics; Logarithm; Sobolev inequality; Unitary state; Inequality; Eigenvalues and eigenvectors; Random matrix; Mathematical analysis; Pure mathematics; Sobolev space","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":true,"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":[0.001855826,0.0005302416,0.000668906,0.002209021,0.0005716338,0.001563442,0.0009115249,0.0008441492,0.005209294],"category_scores_gemma":[0.009768006,0.000222431,0.0005321038,0.0009132748,0.002350718,0.00332122,0.001659866,0.001530506,0.0005165716],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001040851,"about_ca_system_score_gemma":0.0003756484,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009675421,"about_ca_topic_score_gemma":0.000423668,"domain_scores_codex":[0.9986474,0.0004529312,0.00004698266,0.000215702,0.0004803315,0.0001565784],"domain_scores_gemma":[0.9943064,0.003678526,0.0004613973,0.0004325301,0.0007583717,0.0003627702],"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":[0.00003209555,0.000006676116,0.0002322363,0.00004449821,0.000009427979,0.00009703291,0.00006736681,0.005888052,0.00261865,0.9839615,0.000665585,0.006377018],"study_design_scores_gemma":[0.00000703186,0.00003035199,0.0008292948,0.00002336575,0.000007505391,0.0001646546,0.00003401866,0.1048421,0.001616134,0.8894758,0.002942919,0.00002690361],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2415222,0.00321183,0.6659944,0.003561664,0.0003425805,0.00004268929,0.0004493873,0.0002951449,0.08458007],"genre_scores_gemma":[0.9681011,0.0008138536,0.02077337,0.0003581198,0.0004069658,0.0000407542,0.000150324,0.00008615503,0.009269299],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005209294,"threshold_uncertainty_score":0.01742685,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04096997873260017,"score_gpt":0.2598034887072429,"score_spread":0.2188335099746427,"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."}}