{"id":"W2091816855","doi":"10.1007/s00440-010-0328-1","title":"Properties of isoperimetric, functional and Transport-Entropy inequalities via concentration","year":2010,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"University of Toronto","keywords":"Mathematics; Isoperimetric inequality; Sobolev inequality; Concentration of measure; Ricci curvature; Bounded function; Entropy (arrow of time); Curvature; Logarithm; Upper and lower bounds; Mathematical analysis; Sobolev space; Geometry; Thermodynamics","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":[0.00123811,0.0001119897,0.0002434341,0.00006615541,0.0000854169,0.00001497598,0.00004992267,0.0002816701,0.000446868],"category_scores_gemma":[0.0005920887,0.00007587318,0.00006784304,0.0002607081,0.0002546181,0.000128242,0.00001739007,0.0003747384,0.000001109429],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000437164,"about_ca_system_score_gemma":0.00002075429,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001552869,"about_ca_topic_score_gemma":0.00001204563,"domain_scores_codex":[0.9990416,0.0001416568,0.0003725431,0.0001892051,0.0001399383,0.000115086],"domain_scores_gemma":[0.9992746,0.0002846634,0.0001101102,0.0001652117,0.0001147389,0.00005065865],"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":[0.0002389596,0.000224526,0.006520839,0.0003314802,0.0001713153,7.580315e-7,0.002666149,0.000009853201,0.01064657,0.9767382,0.00003097974,0.002420404],"study_design_scores_gemma":[0.0005336778,0.0001232832,0.004482169,0.00003004001,0.0001890819,0.00001501464,0.0004517883,0.0004954495,0.00961416,0.9837517,0.0001421913,0.000171404],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9913792,0.0008232767,0.00601271,0.0001923904,0.0001466318,0.0002065753,0.000003088629,0.00002888058,0.001207235],"genre_scores_gemma":[0.9989091,0.00006086045,0.0004559095,0.00002522577,0.00002520125,0.000007126003,0.000005189065,0.000005799828,0.000505625],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007529852,"threshold_uncertainty_score":0.4892891,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02511751649906387,"score_gpt":0.23204619992877,"score_spread":0.2069286834297061,"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."}}