{"id":"W4406599325","doi":"10.28924/2291-8639-23-2025-15","title":"Central Limit Theorem for Markov Chains with Variable Memory via the Chen-Stein Method","year":2025,"lang":"en","type":"article","venue":"International Journal of Analysis and Applications","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Markov chain; Central limit theorem; Limit (mathematics); Stein's method; Variable (mathematics); Chen; Mathematical economics; Applied mathematics; Calculus (dental); Discrete mathematics; Statistics; Mathematical analysis; Medicine","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001468949,0.000116547,0.0003002832,0.0002761316,0.0001363467,0.00008902407,0.0004085566,0.00004802815,0.00002446076],"category_scores_gemma":[0.0001444091,0.00006936375,0.0002566534,0.0004733189,0.00005965239,0.00006633305,0.00005215509,0.0001413049,1.75629e-8],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005387342,"about_ca_system_score_gemma":0.00008091852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000230096,"about_ca_topic_score_gemma":0.00006153712,"domain_scores_codex":[0.9988993,0.0001109716,0.000446541,0.0001541042,0.0002531158,0.0001359342],"domain_scores_gemma":[0.9974598,0.001169728,0.0004032181,0.0002260802,0.0006796857,0.00006152788],"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":[0.0002116365,0.0002631432,0.0008759613,0.00003919374,0.007462554,0.000002345863,0.0004453096,0.0007686546,0.001513764,0.8737028,0.001489552,0.1132251],"study_design_scores_gemma":[0.00580187,0.0003777425,0.003568226,0.0003320905,0.01997924,0.0002205326,0.005520601,0.1466388,0.01139358,0.4646343,0.3405869,0.000946113],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.002192133,0.000185143,0.9899335,0.003367926,0.00007143679,0.0002588113,0.00003009064,0.000007888048,0.003953077],"genre_scores_gemma":[0.2662398,0.0002194601,0.7261014,0.0009278154,0.0006236044,0.0001977247,0.00002098364,0.00002183698,0.005647368],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4090685,"threshold_uncertainty_score":0.2828571,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01766722477406497,"score_gpt":0.3474946098018499,"score_spread":0.329827385027785,"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."}}