{"id":"W2093019174","doi":"10.1214/aop/1020107774","title":"On the Nonuniqueness of the Invariant Probability for I.I.D. Random Logisitc Maps","year":2002,"lang":"en","type":"article","venue":"The Annals of Probability","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Independent and identically distributed random variables; Random variable; Combinatorics; Markov chain; Invariant (physics); Lambda; Discrete mathematics; Statistics; Mathematical physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.008708836,0.0008520043,0.001980271,0.002604933,0.003044019,0.004193254,0.002505972,0.003013975,0.002940606],"category_scores_gemma":[0.04375384,0.001134318,0.001628514,0.001280996,0.01248995,0.006462923,0.003641592,0.004706359,0.0003823981],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003332788,"about_ca_system_score_gemma":0.001298934,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001853795,"about_ca_topic_score_gemma":0.001344068,"domain_scores_codex":[0.9974186,0.0009813479,0.0001266373,0.000612967,0.0004470145,0.000413297],"domain_scores_gemma":[0.9602492,0.02733136,0.00453895,0.003483529,0.00162479,0.002772179],"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":[0.00005509393,0.00001979215,0.0007207594,0.00002975521,0.00001235796,0.0001239566,0.0001445469,0.004827044,0.0003180531,0.9919918,0.0004329182,0.001323961],"study_design_scores_gemma":[0.0000638243,0.00004985458,0.001056793,0.00002912016,0.00001660539,0.000277119,0.00008451235,0.1151905,0.0005242706,0.8815747,0.001082901,0.00004989449],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5623645,0.002104737,0.3868643,0.006226308,0.0002629441,0.00008687985,0.0004620198,0.0003301633,0.04129827],"genre_scores_gemma":[0.9759423,0.0008874887,0.01797115,0.0004041069,0.0003029384,0.0001476284,0.0001848612,0.00009552528,0.004064008],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008708836,"threshold_uncertainty_score":0.04605728,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2715195442939053,"score_gpt":0.3481491886978063,"score_spread":0.07662964440390096,"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."}}