{"paper":{"title":"Limit processes for TASEP with shocks and rarefaction fans","arxiv_id":"1002.3476","primary_cat":"math-ph","submitted_at":"2010-02-18T10:33:22+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":0.67,"id":"s0","own":false,"role":"background","text":"We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+.","hedge":{"p":0.89,"label":"asserted"},"own_p":0.49,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.67,"limitation":0.0,"future_work":0.0,"contribution":0.3,"interpretation":0.0}},{"i":1,"p":0.43,"id":"s1","own":false,"role":"background","text":"We consider the associated height function, whose discrete gradient is given by the particle occurrences.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.36,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.33,"result":0.0,"background":0.43,"limitation":0.0,"future_work":0.0,"contribution":0.24,"interpretation":0.0}},{"i":2,"p":0.84,"id":"s2","own":false,"role":"background","text":"Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of rho_{+/-}.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.14,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.14,"background":0.84,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.02}},{"i":3,"p":0.78,"id":"s3","own":true,"role":"result","text":"We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.54,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.78,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.22,"interpretation":0.0}},{"i":4,"p":0.58,"id":"s4","own":true,"role":"limitation","text":"Moreover, using a slow decorrelation phenomena, the results are extended from fixed time to the whole space-time, except along the some directions (the characteristic solutions of the related Burgers equation) where the problem is still open.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.2,"background":0.0,"limitation":0.58,"future_work":0.0,"contribution":0.17,"interpretation":0.0}},{"i":5,"p":0.51,"id":"s5","own":true,"role":"result","text":"On the way to proving the results for TASEP, we obtain the limit processes for the fluctuations in a class of corner growth processes with external sources, of equivalently for the last passage time in a directed percolation model with two-sided boundary conditions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.51,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.45,"interpretation":0.0}},{"i":6,"p":0.61,"id":"s6","own":true,"role":"result","text":"Additionally, we provide analogous results for eigenvalues of perturbed complex Wishart (sample covariance) matrices.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.61,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.39,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions.","location":"abstract s3","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":5662,"cost_usd_reported":0.000238},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.03,"states_limitation":0.95,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.02,"states_quantitative_result":0.1,"compares_with_prior_results":0.07,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.89,"text":"We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions.","location":"abstract s3"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":7,"sentences_in_abstract":7},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}