{"id":"W2415796450","doi":"","title":"Invariant and reversible measures for random walks on Z","year":2014,"lang":"en","type":"article","venue":"","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Random walk; Mathematics; Stochastic process; Invariant (physics); Statistical physics; Property (philosophy); Heterogeneous random walk in one dimension; Combinatorics; Discrete mathematics; Statistics; Physics; Mathematical 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009183778,0.0006351456,0.0005689673,0.001577295,0.0008334431,0.002067717,0.0007863303,0.0008921407,0.003953587],"category_scores_gemma":[0.003368541,0.0002847798,0.001093433,0.0007395712,0.00254497,0.002974707,0.001063746,0.001397747,0.0003881214],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000776606,"about_ca_system_score_gemma":0.0004644076,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005876088,"about_ca_topic_score_gemma":0.0005116333,"domain_scores_codex":[0.9993468,0.0001530838,0.00004578092,0.0001324159,0.0002241103,0.00009783749],"domain_scores_gemma":[0.9985323,0.00065728,0.000392987,0.0001256564,0.0001303437,0.0001615076],"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":[0.000005076903,0.00001257423,0.0002125673,0.00002861133,0.000005982836,0.00009884477,0.00006736084,0.001713813,0.0008961858,0.9951521,0.0001736478,0.001633278],"study_design_scores_gemma":[0.00001494704,0.00006239471,0.0009219719,0.00002452196,0.0000117888,0.0002796785,0.0001090734,0.03341607,0.0008968697,0.9614758,0.002764478,0.00002247922],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5394048,0.003986847,0.3754051,0.001977517,0.0005306166,0.0001186052,0.0003273651,0.0001487151,0.07810055],"genre_scores_gemma":[0.9539717,0.002593261,0.02919479,0.0002549123,0.0005213301,0.0001164791,0.000210873,0.0000723289,0.01306442],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003953587,"threshold_uncertainty_score":0.01322603,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05538520759041796,"score_gpt":0.3045512905953977,"score_spread":0.2491660830049797,"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."}}