{"abstract":[{"text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ&lt;λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.","lang":"eng"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"quality_controlled":"1","scopus_import":"1","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"isi":1,"author":[{"first_name":"Patrick","last_name":"Ferrari","full_name":"Ferrari, Patrick"},{"last_name":"Ghosal","full_name":"Ghosal, Promit","first_name":"Promit"},{"last_name":"Nejjar","full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"}],"citation":{"ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>.","apa":"Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>."},"intvolume":"        55","ec_funded":1,"status":"public","title":"Limit law of a second class particle in TASEP with non-random initial condition","date_created":"2018-12-11T11:44:29Z","oa_version":"Preprint","date_published":"2019-09-25T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","article_type":"original","type":"journal_article","publication_identifier":{"issn":["0246-0203"]},"month":"09","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","_id":"72","date_updated":"2023-10-17T08:53:45Z","main_file_link":[{"url":"https://arxiv.org/abs/1710.02323","open_access":"1"}],"page":"1203-1225","issue":"3","doi":"10.1214/18-AIHP916","external_id":{"isi":["000487763200001"],"arxiv":["1710.02323"]},"publication_status":"published","language":[{"iso":"eng"}],"oa":1,"publisher":"Institute of Mathematical Statistics","volume":55,"year":"2019","day":"25"}