{"id":"W2950320606","doi":"10.1215/00127094-2010-216","title":"Random walks on the mapping class group","year":2011,"lang":"en","type":"article","venue":"Duke Mathematical Journal","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":103,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centre de Recherches Mathématiques; California Institute of Technology; National Science Foundation","keywords":"Mapping class group; Random walk; Group (periodic table); Mathematics; Class (philosophy); Combinatorics; Surface (topology); Element (criminal law); Pure mathematics; Geometry; Statistics; Computer science; Physics; Artificial intelligence","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005999234,0.0004913735,0.0005484761,0.001209057,0.00090685,0.001585366,0.0006870921,0.001078849,0.004130111],"category_scores_gemma":[0.003843205,0.0002636905,0.0006960436,0.0004606048,0.001741741,0.00219021,0.001447192,0.001207078,0.0004883566],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005056915,"about_ca_system_score_gemma":0.0002382669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005852244,"about_ca_topic_score_gemma":0.0003850644,"domain_scores_codex":[0.9996307,0.0001063592,0.00001217959,0.00007132313,0.00009763288,0.00008183051],"domain_scores_gemma":[0.9982758,0.0008993503,0.0002647247,0.0001924465,0.0001196678,0.0002479669],"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":[0.00004954029,0.00002277388,0.0008154531,0.00003023962,0.00001379118,0.0002993,0.0001840996,0.009309167,0.002660148,0.9824118,0.0007124406,0.003491259],"study_design_scores_gemma":[0.00004256029,0.00006665703,0.0009775657,0.00001827199,0.00001501403,0.0003253325,0.0001190849,0.1839995,0.002092095,0.8094446,0.00286199,0.00003723229],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7095742,0.0005970232,0.2595734,0.001171884,0.0002674533,0.00006706705,0.0001328305,0.0002786113,0.02833747],"genre_scores_gemma":[0.9769065,0.0003843156,0.01205432,0.000154206,0.0002404309,0.00007519057,0.0001052397,0.00007263989,0.01000706],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004130111,"threshold_uncertainty_score":0.01381665,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.113506317733412,"score_gpt":0.2798542629857488,"score_spread":0.1663479452523368,"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."}}