{"id":"W2017565711","doi":"10.1007/s00220-011-1251-8","title":"Spectral Dimension and Random Walks on the Two Dimensional Uniform Spanning Tree","year":2011,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Random walk; Mathematics; Combinatorics; Spanning tree; Euclidean minimum spanning tree; Dimension (graph theory); Shortest-path tree; Loop-erased random walk; Minimum spanning tree; Euclidean geometry; Tree (set theory); Random graph; Random tree; Graph; Euclidean distance; Discrete mathematics; Minimum degree spanning tree; Geometry; Statistics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0006071667,0.0001999512,0.0003268169,0.00004102761,0.0002635177,0.00003079044,0.0005927503,0.00005832521,0.000100749],"category_scores_gemma":[0.001401185,0.0001322266,0.00006281774,0.0002301037,0.0002984254,0.00007731307,0.0004092434,0.0004565495,0.00005815837],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004107707,"about_ca_system_score_gemma":0.00002744634,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006408571,"about_ca_topic_score_gemma":0.00001047495,"domain_scores_codex":[0.9987247,0.0001194139,0.000429248,0.000202239,0.0002604805,0.0002639489],"domain_scores_gemma":[0.9933406,0.005149299,0.000119741,0.001237459,0.00007218788,0.0000807902],"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":[0.00003868809,0.0004340489,0.000007302279,0.00003919292,0.00001794838,0.000001940533,0.001242409,0.000006233191,0.00006148579,0.9945269,0.0001035203,0.003520375],"study_design_scores_gemma":[0.000644887,0.00006457032,0.00005780423,0.0002097081,0.00004273442,0.000007818566,0.0002008586,0.09920788,0.0002392186,0.8991622,0.00001596074,0.0001463008],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0947859,0.0002007975,0.7994872,0.002960101,0.0001344294,0.001611673,0.00003095532,0.0002242886,0.1005647],"genre_scores_gemma":[0.8318338,0.00001761516,0.1677429,0.0002006484,0.00002639781,0.00007560005,0.000004644408,0.00002859266,0.00006977284],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7370479,"threshold_uncertainty_score":0.5392043,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1347383039528844,"score_gpt":0.3460315260683617,"score_spread":0.2112932221154774,"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."}}