{"id":"W2783781429","doi":"10.48550/arxiv.1801.03386","title":"Asymptotics of the density of parabolic Anderson random fields","year":2018,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Leverhulme Trust; University of Alberta","keywords":"Multiplicative function; Combinatorics; Upper and lower bounds; Mathematical physics; Physics; Product (mathematics); Gaussian; Modulo; Mathematics; Mathematical analysis; Quantum mechanics; 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":[0.0022119,0.0007282256,0.0007355448,0.001930975,0.0007575047,0.00151188,0.001826201,0.001453059,0.004234544],"category_scores_gemma":[0.01454055,0.0007266444,0.0006541275,0.0006131109,0.004050552,0.00278608,0.002361809,0.002092149,0.0004473973],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001999681,"about_ca_system_score_gemma":0.0009976133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005697038,"about_ca_topic_score_gemma":0.002316996,"domain_scores_codex":[0.9995099,0.0001760296,0.00001748885,0.0000910485,0.000101242,0.0001042274],"domain_scores_gemma":[0.9948219,0.002606042,0.0007152873,0.0003790893,0.0006230998,0.0008546531],"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":[0.0001605759,0.00008355047,0.003730748,0.0001776731,0.00005570483,0.0004396314,0.0003661099,0.07596192,0.007100622,0.9055353,0.002260231,0.004127813],"study_design_scores_gemma":[0.00003909775,0.00005786805,0.00328888,0.00007779263,0.00003057755,0.000170947,0.0001335324,0.7646857,0.001798913,0.2287716,0.0008656197,0.00007952154],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7289784,0.001506453,0.2377027,0.004683212,0.0001765823,0.0001004166,0.0004348789,0.0009450135,0.02547236],"genre_scores_gemma":[0.9829566,0.0005573184,0.007358424,0.0002707649,0.0001414754,0.0001057066,0.0002671081,0.0001083783,0.008234198],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005697038,"threshold_uncertainty_score":0.01450872,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1053947729377435,"score_gpt":0.2285145935036794,"score_spread":0.1231198205659359,"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."}}