{"id":"W2009720170","doi":"10.1007/s00440-007-0083-0","title":"Infinite volume limit of the Abelian sandpile model in dimensions d ≥  3","year":2007,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Abelian sandpile model; Mathematics; Ergodic theory; Measure (data warehouse); Abelian group; Limit (mathematics); Connection (principal bundle); Markov chain; Pure mathematics; Combinatorics; Mathematical analysis; Discrete mathematics; Statistical physics; Geometry; 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":[],"consensus_categories":[],"category_scores_codex":[0.001724859,0.0000982402,0.0001869746,0.0000354703,0.00007197469,0.000005586692,0.0001201401,0.000260379,0.00006083915],"category_scores_gemma":[0.002719315,0.00006293622,0.00005071091,0.0002065085,0.0001442357,0.00003298673,0.00009685772,0.0003965208,0.000001863494],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001342091,"about_ca_system_score_gemma":0.0000332903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004834028,"about_ca_topic_score_gemma":0.00003051134,"domain_scores_codex":[0.9990478,0.00008600498,0.0003995653,0.0001684377,0.0001112388,0.0001869603],"domain_scores_gemma":[0.9980952,0.001443385,0.00008616676,0.0002633948,0.00005782719,0.00005401781],"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":[0.000107399,0.0001322553,0.0002133972,0.0001242289,0.00001317511,0.000001404615,0.001248801,0.0001692641,0.0001076154,0.9961904,0.00003576573,0.001656348],"study_design_scores_gemma":[0.0002567318,0.00005976146,0.0002920218,0.00008724254,0.0000319994,0.000005031558,0.00009589735,0.02093851,0.0002448432,0.9778891,0.00001928679,0.00007957104],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6989931,0.0002063551,0.2923743,0.0005329125,0.0001755358,0.0004828366,0.00001750419,0.00003928522,0.007178165],"genre_scores_gemma":[0.9952214,0.00001937218,0.004219432,0.00007731857,0.000005114764,0.000004601458,6.156942e-7,0.000007411561,0.0004447357],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2962283,"threshold_uncertainty_score":0.325547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02532247341522312,"score_gpt":0.278017501083902,"score_spread":0.2526950276686789,"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."}}