{"id":"W1971911267","doi":"10.1016/j.jfa.2012.02.004","title":"Short-time asymptotics of heat kernels of hypoelliptic Laplacians on unimodular Lie groups","year":2012,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; Fonds Québécois de la Recherche sur la Nature et les Technologies","keywords":"Hypoelliptic operator; Mathematics; Unimodular matrix; Heat kernel; Lie group; Complexification; Heisenberg group; Pure mathematics; Simple Lie group; Nilpotent; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001984046,0.001237134,0.001413585,0.00403116,0.001838299,0.002854419,0.002460168,0.002144768,0.007599591],"category_scores_gemma":[0.01170367,0.0008371805,0.001044233,0.00108216,0.004885779,0.006236762,0.00300627,0.002795517,0.0006224888],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002261932,"about_ca_system_score_gemma":0.0009963271,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002928834,"about_ca_topic_score_gemma":0.00248135,"domain_scores_codex":[0.9994389,0.0001550274,0.00002769118,0.00008088948,0.0001319535,0.0001654616],"domain_scores_gemma":[0.9945392,0.001494312,0.0007599409,0.0003553242,0.0009260302,0.001925163],"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":[0.0002281056,0.0001459927,0.001685704,0.0001276842,0.00004971384,0.0004990558,0.0007711209,0.02098426,0.006649815,0.9633551,0.001420489,0.004082986],"study_design_scores_gemma":[0.00004788529,0.00007570322,0.003220515,0.00004875431,0.00002622744,0.0002578438,0.0004071798,0.3282137,0.001140008,0.6656615,0.0008049054,0.00009577509],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8909883,0.001179637,0.08512343,0.001857236,0.0003543635,0.00005718291,0.0001546787,0.0006291056,0.01965609],"genre_scores_gemma":[0.982534,0.0004367965,0.005547638,0.0002034119,0.0004883556,0.00005005768,0.000225157,0.0002505186,0.01026409],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007599591,"threshold_uncertainty_score":0.02542317,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04003885956722771,"score_gpt":0.2676277134191234,"score_spread":0.2275888538518957,"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."}}