{"id":"W4315702961","doi":"10.1090/tran/8895","title":"Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices","year":2023,"lang":"lv","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"National Natural Science Foundation of China; National Science Foundation","keywords":"Mathematics; Eigenvalues and eigenvectors; Gaussian; Collision; Random matrix; Random field; Gaussian random field; Statistical physics; Gaussian process; Mathematical analysis; Statistics; Quantum mechanics; 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":[0.001144631,0.0002690624,0.001562723,0.00006831902,0.0001499744,0.00001257745,0.0003943604,0.0001383411,0.0001079477],"category_scores_gemma":[0.00148608,0.0001854544,0.0007356422,0.001075583,0.001636113,0.00006576896,0.00007170569,0.0002589409,0.000001905998],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002492753,"about_ca_system_score_gemma":0.0001244144,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001214851,"about_ca_topic_score_gemma":0.000004424225,"domain_scores_codex":[0.9970869,0.0001740961,0.001502856,0.0002547257,0.000669985,0.0003113929],"domain_scores_gemma":[0.9904321,0.007357739,0.001332752,0.0005087972,0.0002791307,0.00008949604],"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":[0.005324256,0.006794993,0.0003227355,0.1829654,0.006824307,0.000003692323,0.1601187,0.006435724,0.02444912,0.5640647,0.001412249,0.0412841],"study_design_scores_gemma":[0.003804553,0.001081467,0.0001717058,0.003093944,0.002260743,0.00001151574,0.03460477,0.1593203,0.02713431,0.7681324,0.000007774267,0.0003765199],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3091998,0.000269559,0.6887668,0.0003777748,0.00007232452,0.000769199,0.0003295149,0.0000307509,0.0001842789],"genre_scores_gemma":[0.934768,0.0007736075,0.06419395,0.00001200822,0.00001688111,0.00003144403,0.000001355101,0.00003191368,0.0001708663],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6255682,"threshold_uncertainty_score":0.7562613,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02442103824131122,"score_gpt":0.295228438271938,"score_spread":0.2708074000306268,"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."}}