{"page":"1311-1334","oa_version":"Published Version","isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Instituto Nacional de Matematica Pura e Aplicada","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes."}],"oa":1,"external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"has_accepted_license":"1","year":"2018","language":[{"iso":"eng"}],"date_updated":"2023-10-10T13:11:29Z","day":"01","intvolume":"        15","article_type":"original","publication_identifier":{"issn":["1980-0436"]},"publication":"Latin American Journal of Probability and Mathematical Statistics","ec_funded":1,"doi":"10.30757/ALEA.v15-49","date_published":"2018-10-01T00:00:00Z","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"title":"Transition to shocks in TASEP and decoupling of last passage times","scopus_import":"1","date_created":"2018-12-11T11:44:28Z","file_date_updated":"2020-07-14T12:47:46Z","citation":{"ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. <i>Latin American Journal of Probability and Mathematical Statistics</i>. 2018;15(2):1311-1334. doi:<a href=\"https://doi.org/10.30757/ALEA.v15-49\">10.30757/ALEA.v15-49</a>","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>. Instituto Nacional de Matematica Pura e Aplicada, 2018. <a href=\"https://doi.org/10.30757/ALEA.v15-49\">https://doi.org/10.30757/ALEA.v15-49</a>.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. <i>Latin American Journal of Probability and Mathematical Statistics</i>. Instituto Nacional de Matematica Pura e Aplicada. <a href=\"https://doi.org/10.30757/ALEA.v15-49\">https://doi.org/10.30757/ALEA.v15-49</a>","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:<a href=\"https://doi.org/10.30757/ALEA.v15-49\">10.30757/ALEA.v15-49</a>.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” <i>Latin American Journal of Probability and Mathematical Statistics</i>, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334."},"author":[{"full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Nejjar"}],"month":"10","file":[{"file_name":"2018_ALEA_Nejjar.pdf","access_level":"open_access","checksum":"2ded46aa284a836a8cbb34133a64f1cb","content_type":"application/pdf","creator":"kschuh","date_updated":"2020-07-14T12:47:46Z","file_size":394851,"relation":"main_file","date_created":"2019-02-14T09:44:10Z","file_id":"5981"}],"_id":"70","status":"public","volume":15,"quality_controlled":"1","publication_status":"published","issue":"2","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"article_processing_charge":"No","ddc":["510"],"type":"journal_article"}