{"id":"W4298306018","doi":"10.48550/arxiv.1409.7975","title":"The smallest singular value of random rectangular matrices with no\\n moment assumptions on entries","year":2014,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Combinatorics; Mathematics; Random matrix; Lambda; Singular value; Distribution (mathematics); Moment (physics); Matrix (chemical analysis); Second moment of area; Physics; Mathematical analysis; Geometry; Eigenvalues and eigenvectors; Quantum mechanics","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":[0.00307939,0.002309685,0.001254157,0.001640146,0.0008445168,0.00233498,0.001727988,0.001613613,0.00500534],"category_scores_gemma":[0.02678449,0.0008710349,0.0009709931,0.0008621378,0.006013942,0.00417638,0.002278974,0.003000763,0.001342035],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001384404,"about_ca_system_score_gemma":0.002371974,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001459278,"about_ca_topic_score_gemma":0.001207879,"domain_scores_codex":[0.9977885,0.0006658971,0.00009483808,0.000618182,0.0004372736,0.0003952616],"domain_scores_gemma":[0.9825069,0.01088931,0.002304486,0.00155569,0.00127249,0.0014711],"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":[0.001028619,0.0001989197,0.002893717,0.0009576746,0.000242352,0.0007491518,0.0003827497,0.1241564,0.02740706,0.8092068,0.008475905,0.02430077],"study_design_scores_gemma":[0.00008249806,0.0003400348,0.002152674,0.0002374133,0.00005998023,0.0004397747,0.0002008156,0.5629401,0.0120703,0.4185383,0.002772883,0.0001652138],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1840355,0.002141202,0.7886178,0.002370764,0.0003922335,0.0001825499,0.001242999,0.0007744542,0.02024239],"genre_scores_gemma":[0.9040402,0.002715964,0.07497075,0.0007393479,0.0006471887,0.0004850022,0.001444269,0.0003507608,0.01460648],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00500534,"threshold_uncertainty_score":0.01674449,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03989284838240364,"score_gpt":0.1997885442588037,"score_spread":0.1598956958764,"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."}}