{"id":"W2132643508","doi":"10.4153/cjm-2004-010-6","title":"A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations","year":2004,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Law of the iterated logarithm; Iterated logarithm; Central limit theorem; Logarithm; Mixing (physics); Law of large numbers; Lemma (botany); Iterated function; Mathematical proof; Exponential function; Field (mathematics); Limit (mathematics); Pure mathematics; Random variable; Law; Discrete mathematics; Mathematical analysis; Statistics; Quantum mechanics; Geometry","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":[0.0002432434,0.00009841847,0.0003242293,0.00005758581,0.00008546705,0.00002125744,0.0001567585,0.00006477764,0.00001974364],"category_scores_gemma":[0.001253815,0.00006022782,0.00008075263,0.0001050542,0.0001263582,0.00004662596,0.000009412209,0.000122834,1.0105e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003026953,"about_ca_system_score_gemma":0.0005072572,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001764239,"about_ca_topic_score_gemma":0.004434434,"domain_scores_codex":[0.9991074,0.00001643284,0.0004820458,0.00005783043,0.0001551805,0.0001811302],"domain_scores_gemma":[0.9980063,0.0008999854,0.0004367517,0.0001292911,0.0003444654,0.0001832278],"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":[0.00007012698,0.00006111684,0.00001264807,0.0003077451,0.00008542156,0.000009897442,0.002655712,0.0001093772,0.000076613,0.9963554,0.00006821476,0.0001877177],"study_design_scores_gemma":[0.003523191,0.0005731424,0.00002782995,0.001123473,0.0004010676,0.0003121585,0.001103605,0.003039095,0.004968242,0.9847559,0.00005312,0.0001192281],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0807732,0.00008697017,0.9180645,0.0003185017,0.0001201405,0.0002857834,0.00007860744,0.000002156341,0.0002700853],"genre_scores_gemma":[0.9102722,0.000003136542,0.08961786,0.00004534117,0.00002773004,0.000003168712,6.121511e-7,0.00001342695,0.00001647979],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8294991,"threshold_uncertainty_score":0.2474518,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02202045867789769,"score_gpt":0.2479046349767313,"score_spread":0.2258841762988336,"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."}}