{"id":"W4300796208","doi":"","title":"Random walks in the quarter plane absorbed at the boundary: exact and asymptotic","year":2009,"lang":"en","type":"preprint","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Quarter (Canadian coin); Random walk; Boundary (topology); Plane (geometry); Mathematics; Statistical physics; Physics; Statistics; Mathematical analysis; Geometry; Geography","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006497014,0.0003119337,0.0004284412,0.00007527332,0.0004073305,0.0004492586,0.001010336,0.0002224795,0.000124404],"category_scores_gemma":[0.004071228,0.000200728,0.0001094296,0.0001860496,0.000221041,0.00004523029,0.0005924965,0.0007632567,0.00002241317],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008479632,"about_ca_system_score_gemma":0.000131927,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000215901,"about_ca_topic_score_gemma":0.002195741,"domain_scores_codex":[0.9949577,0.003167927,0.0005305254,0.0005185701,0.0004800555,0.0003452437],"domain_scores_gemma":[0.988126,0.009490691,0.0003409681,0.001538803,0.0004134477,0.00009006443],"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":[0.0001536329,0.0007555601,0.000121571,0.0006113949,0.0001189745,0.00003037792,0.03498632,0.00001782868,0.0002025199,0.9150278,0.008891142,0.03908288],"study_design_scores_gemma":[0.002045358,0.000002552202,0.001844062,0.001836344,0.0001634933,0.00007736535,0.0005739258,0.02457504,0.0006631833,0.9622933,0.005378246,0.0005471276],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09681585,0.003304644,0.8224151,0.03798966,0.0003217561,0.002065015,0.0002012829,0.0001898062,0.03669694],"genre_scores_gemma":[0.9746599,0.000507336,0.02180511,0.0004673319,0.00003845332,0.0001461858,0.0001997283,0.00004605265,0.002129878],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.877844,"threshold_uncertainty_score":0.8185451,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01841653657615526,"score_gpt":0.2582385106788197,"score_spread":0.2398219741026644,"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."}}