{"id":"W2023503064","doi":"10.1239/aap/1134587754","title":"Light-tailed asymptotics of stationary probability vectors of Markov chains of GI/G/1 type","year":2005,"lang":"en","type":"article","venue":"Advances in Applied Probability","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":44,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Markov chain; Generating function; Boundary (topology); Type (biology); Markov process; Stationary distribution; Function (biology); Factorization; Markov property; Continuous-time Markov chain; Probability measure; Combinatorics; Mathematical analysis; Markov model; Statistics; Algorithm","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001316286,0.0006026548,0.0007216584,0.001786031,0.0007264962,0.001207021,0.001011199,0.0008222826,0.003986662],"category_scores_gemma":[0.01033652,0.0003169027,0.0007352129,0.0006649582,0.002562059,0.002413882,0.0008949899,0.001593248,0.0006271026],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001082989,"about_ca_system_score_gemma":0.0006988611,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001621593,"about_ca_topic_score_gemma":0.001059254,"domain_scores_codex":[0.9995284,0.0001361295,0.00002161932,0.000081196,0.0001190132,0.0001137083],"domain_scores_gemma":[0.9964993,0.00166306,0.0006193547,0.0002264109,0.0006370348,0.0003547857],"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":[0.00005952558,0.00004803173,0.002437226,0.00009904203,0.00002582485,0.0004291071,0.0002891068,0.03032476,0.005512009,0.9531741,0.0009910386,0.006610233],"study_design_scores_gemma":[0.00001801441,0.0000653469,0.001786807,0.00004906716,0.00001612155,0.0003135927,0.0001241526,0.465133,0.002662519,0.5288171,0.0009613079,0.00005293856],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5464624,0.001124075,0.4320992,0.0008081875,0.0001293453,0.00009644718,0.0001607587,0.0005126364,0.0186069],"genre_scores_gemma":[0.9780431,0.0005840003,0.01515713,0.0001525877,0.0001397174,0.00009743097,0.0002049533,0.0001138816,0.005507218],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003986662,"threshold_uncertainty_score":0.01333672,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02173070201576017,"score_gpt":0.3048411476030417,"score_spread":0.2831104455872815,"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."}}