{"id":"W4311175942","doi":"10.1080/00029890.2022.2144088","title":"Random Walks, Directed Cycles, and Markov Chains","year":2022,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Acadia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Markov chain; Random walk; Examples of Markov chains; Mathematics; Variable-order Markov model; Discrete phase-type distribution; Markov renewal process; Markov process; Markov property; Markov chain mixing time; Markov kernel; Absorbing Markov chain; Discrete mathematics; Markov model; Limiting; Statistical physics; Statistics; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001429301,0.0003467044,0.0009177762,0.0001474644,0.0003869713,0.00005213808,0.0003353166,0.00004460069,0.0003612716],"category_scores_gemma":[0.001414594,0.0003043899,0.0001970979,0.0004684055,0.000390299,0.00006305023,0.0004789909,0.0004218533,8.742381e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001064685,"about_ca_system_score_gemma":0.00004556598,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008596388,"about_ca_topic_score_gemma":0.0000196934,"domain_scores_codex":[0.9970633,0.0006906244,0.0005938109,0.00051276,0.000584109,0.0005554154],"domain_scores_gemma":[0.9963251,0.00237936,0.0002946043,0.0006462465,0.00005472569,0.0002999232],"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":[0.001189798,0.0023332,0.001174268,0.0008553895,0.0006791615,0.0003744559,0.008498592,0.00003569276,0.002148369,0.8447522,0.04459286,0.09336603],"study_design_scores_gemma":[0.008872521,0.001651478,0.001753502,0.0002059145,0.0007421329,0.0003792397,0.01494391,0.08191565,0.0004740357,0.8261685,0.05991538,0.002977687],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6032885,0.0008539682,0.03416431,0.003401179,0.0004147739,0.002467642,0.0002974692,0.001634059,0.3534782],"genre_scores_gemma":[0.7429857,0.00004710443,0.2505505,0.0008795009,0.0001445599,0.0006332974,0.00001959156,0.0001499017,0.004589748],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3488884,"threshold_uncertainty_score":0.9999408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0249556212225725,"score_gpt":0.3064007245783991,"score_spread":0.2814451033558266,"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."}}