{"id":"W2727382962","doi":"","title":"Random walks in the quarter plane, harmonic functions and conformal mappings","year":2013,"lang":"en","type":"article","venue":"arXiv (Cornell University)","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Harmonic function; Mathematics; Harmonic; Conformal map; Corollary; Uniqueness; Harmonic measure; Plane (geometry); Random walk; Mathematical analysis; Function (biology); Complex plane; Quarter (Canadian coin); Subharmonic function; Pure mathematics; Physics; Geometry; Quantum mechanics; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004760369,0.0002913034,0.000409859,0.0008031199,0.0003265634,0.0008657058,0.0004285388,0.0005273146,0.001711823],"category_scores_gemma":[0.001858113,0.0001737765,0.0002963502,0.0003601649,0.001064071,0.001206599,0.0005309616,0.0004750386,0.0002481723],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004778992,"about_ca_system_score_gemma":0.0002691862,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006051905,"about_ca_topic_score_gemma":0.0003981806,"domain_scores_codex":[0.999895,0.0000381511,0.000004636381,0.00001540823,0.00002824292,0.00001858596],"domain_scores_gemma":[0.9996029,0.0001554153,0.00007856536,0.00004626991,0.00006226855,0.00005457983],"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":[0.0000361066,0.00002069149,0.0009335767,0.00003313575,0.0000101954,0.0001069686,0.000071937,0.03019034,0.005098172,0.9570444,0.0006816576,0.005772896],"study_design_scores_gemma":[0.00001864991,0.00003546973,0.0009664277,0.00001253644,0.000005894625,0.0002119543,0.00008034948,0.3963792,0.001612799,0.5991775,0.001482015,0.00001723205],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5573388,0.0009391378,0.4218352,0.0008396999,0.0001259412,0.00004487752,0.0001861745,0.0001808293,0.01850934],"genre_scores_gemma":[0.9715774,0.0003630898,0.02072575,0.0001014914,0.00005758963,0.00003107667,0.00008135144,0.0000510596,0.007011182],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001711823,"threshold_uncertainty_score":0.005726576,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01974938828999088,"score_gpt":0.1458330792310238,"score_spread":0.1260836909410329,"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."}}