{"id":"W1892120934","doi":"10.1214/18-aop1258","title":"Structure of optimal martingale transport plans in general dimensions","year":2018,"lang":"en","type":"preprint","venue":"The Annals of Probability","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; University of British Columbia; ShanghaiTech University; Austrian Science Fund; European Commission","keywords":"Probability measure; Martingale (probability theory); Mathematics; Lebesgue measure; Combinatorics; Disjoint sets; Absolute continuity; Measure (data warehouse); Borel measure; Countable set; Convex hull; Random measure; Discrete mathematics; Regular polygon; Lebesgue integration; Pure mathematics; Applied mathematics; Computer science; Geometry","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":[0.001975266,0.0008350263,0.001371178,0.002446092,0.001239458,0.003386658,0.001699399,0.001948143,0.005019926],"category_scores_gemma":[0.006994235,0.001070791,0.001372316,0.001197099,0.003723553,0.003594504,0.00215927,0.002024271,0.0005038691],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004833486,"about_ca_system_score_gemma":0.001836123,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002947282,"about_ca_topic_score_gemma":0.002456054,"domain_scores_codex":[0.9990972,0.0002347884,0.00005119871,0.0001837586,0.000204113,0.0002288553],"domain_scores_gemma":[0.9965972,0.001232251,0.000758473,0.0002063263,0.0003681497,0.0008376344],"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":[0.00009016469,0.00004205198,0.001542137,0.00005851756,0.00003286932,0.0001403893,0.0001521376,0.05864435,0.001534179,0.9342746,0.0006793618,0.002809127],"study_design_scores_gemma":[0.00005811851,0.0001361562,0.002060825,0.00005898799,0.00002297653,0.00008647172,0.0001382452,0.3521547,0.001134906,0.642745,0.00134207,0.00006147408],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.7375028,0.0008684582,0.2423239,0.001678036,0.00005074871,0.0001230038,0.0007370442,0.0004032382,0.01631286],"genre_scores_gemma":[0.9615213,0.000652282,0.02780547,0.0001916774,0.00005364886,0.0002058403,0.000604495,0.000125633,0.008839628],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.005019926,"threshold_uncertainty_score":0.03506958,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1811104262174346,"score_gpt":0.3795210841713995,"score_spread":0.1984106579539649,"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."}}