{"paper":{"title":"Applying Free Random Variables to Random Matrix Analysis of Financial Data. Part I: A Gaussian Case","arxiv_id":"physics/0603024","primary_cat":"physics.soc-ph","submitted_at":"2006-03-04T15:41:27+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":0.88,"id":"s0","own":true,"role":"contribution","text":"We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing for example in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.85,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.1,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":1,"p":0.54,"id":"s1","own":true,"role":"contribution","text":"We give a comprehensive introduction to the rich financial reality behind such models.","hedge":{"p":0.89,"label":"asserted"},"own_p":0.67,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.45,"limitation":0.0,"future_work":0.0,"contribution":0.54,"interpretation":0.0}},{"i":2,"p":0.51,"id":"s2","own":true,"role":"contribution","text":"We explain in an elementary way the main techniques of the free random variables calculus, with a view to promote them in the quantitative finance community.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.8,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.47,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.01,"contribution":0.51,"interpretation":0.0}},{"i":3,"p":0.96,"id":"s3","own":true,"role":"contribution","text":"We apply our findings to tackle several financially relevant problems, such as of an universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.27,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.96,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.83,"text":"We apply our findings to tackle several financially relevant problems, such as of an universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.","location":"abstract s3","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":3668,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.05,"states_limitation":0.15,"human_participants":0.02,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.05,"compares_with_prior_results":0.06,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.01,"literature":0.0,"proof_or_derivation":0.99,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.62,"value":"method or tool","probabilities":{"review":0.03,"method_or_tool":0.62,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.35,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.92,"text":"We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing for example in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances.","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":4,"sentences_in_abstract":4},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}