{"id":"W1984650562","doi":"10.1007/s00440-007-0112-z","title":"Shannon–McMillan theorems for discrete random fields along curves and lower bounds for surface-order large deviations","year":2007,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Theoretical and Computational Physics","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Ergodic theory; Tangent; Entropy (arrow of time); Gibbs measure; Large deviations theory; Statistical physics; Ising model; Phase transition; Random field; Lattice (music); Combinatorics; Mathematical analysis; Geometry; Thermodynamics; Statistics; 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":[0.001509906,0.0001656716,0.0002294771,0.00001717057,0.0003093267,0.00004290547,0.00008295719,0.0001499982,0.0001378234],"category_scores_gemma":[0.00008910471,0.0001269266,0.0001277309,0.00009502955,0.0001898408,0.00008855636,0.00005076708,0.000210972,0.000001457159],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005736041,"about_ca_system_score_gemma":0.00002586935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005930051,"about_ca_topic_score_gemma":0.000004607376,"domain_scores_codex":[0.9989471,0.00009274052,0.0003035685,0.0002928928,0.00007577352,0.0002878735],"domain_scores_gemma":[0.9976833,0.001871796,0.00007245295,0.0001489875,0.0001319008,0.00009149272],"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":[0.0005702915,0.000105214,0.001706722,0.0001061085,0.000117746,1.839709e-7,0.0003964524,0.0001064044,0.00001319843,0.9945009,0.0001292095,0.002247602],"study_design_scores_gemma":[0.001598776,0.0001371166,0.0004697224,0.00005475235,0.00008190744,9.119845e-7,0.0001363091,0.001488427,0.0001451276,0.9947199,0.0009757549,0.0001913078],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3046233,0.0006834453,0.6872851,0.001206578,0.0001987275,0.0009450184,0.0001218168,0.00003783313,0.004898134],"genre_scores_gemma":[0.9985224,0.00003167921,0.0005522458,0.0002098162,0.0001069544,0.00003827333,0.0001231187,0.00001373023,0.0004017957],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.693899,"threshold_uncertainty_score":0.5175915,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005817702131690091,"score_gpt":0.2471277611159009,"score_spread":0.2413100589842108,"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."}}