{"id":"W4297893423","doi":"10.48550/arxiv.1201.0329","title":"Random walks on random horospheric products","year":2012,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Canada Research Chairs","keywords":"Random walk; Mathematics; Poisson distribution; Statistical physics; Equivalence (formal languages); Discrete mathematics; Statistics; Physics","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":[0.001081374,0.0006003323,0.0006917511,0.002161053,0.0009763742,0.003074956,0.001025287,0.0008390644,0.003442896],"category_scores_gemma":[0.004304339,0.0003824454,0.0006076982,0.001003365,0.002877616,0.005370316,0.002096551,0.00146634,0.0003963571],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009638086,"about_ca_system_score_gemma":0.000306584,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005857777,"about_ca_topic_score_gemma":0.0004752559,"domain_scores_codex":[0.9991308,0.0002346073,0.000041574,0.0001480206,0.000292594,0.0001523489],"domain_scores_gemma":[0.9982103,0.0007601543,0.0002862888,0.0001611732,0.0002888042,0.0002933142],"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":[0.000007785539,0.000006430134,0.0002098852,0.000009335843,0.000003041305,0.0000750017,0.00009701545,0.001787284,0.0004773959,0.9963355,0.0001122159,0.0008792134],"study_design_scores_gemma":[0.00000741912,0.00001807868,0.0005222762,0.00001252297,0.000004314789,0.0001205017,0.0001020695,0.03261825,0.0005222613,0.9649769,0.001082743,0.00001257965],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6543686,0.001042352,0.299969,0.001090703,0.0001544167,0.00006669007,0.0001876911,0.0001449825,0.04297552],"genre_scores_gemma":[0.979655,0.0003976371,0.01331019,0.00009614269,0.0001662866,0.00004369908,0.0001158204,0.00006616775,0.006148973],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003442896,"threshold_uncertainty_score":0.01151758,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1223569223203624,"score_gpt":0.2262128196720481,"score_spread":0.1038558973516857,"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."}}