[{"publication_status":"published","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2404.11700","open_access":"1"}],"doi":"10.30757/ALEA.V21-70","isi":1,"OA_type":"green","oa":1,"abstract":[{"lang":"eng","text":"We prove the Central Limit Theorem and superpolynomial mixing for environment\r\nviewed from the particle process in quasi periodic Diophantine random environment. The main\r\ningredients are smoothness estimates for the solution of the Poisson equation and local limit asymptotics for certain accelerated walks."}],"_id":"18586","day":"01","OA_place":"repository","language":[{"iso":"eng"}],"oa_version":"Preprint","issue":"2","status":"public","title":"The central limit theorem and rate of mixing for simple random walks on the circle","department":[{"_id":"VaKa"}],"date_created":"2024-11-24T23:01:49Z","ec_funded":1,"page":"1853-1865","article_type":"original","article_processing_charge":"No","acknowledgement":"ents. The authors are grateful to Agnieszka Zelerowicz and the anonymous referee\r\nfor useful comments. The first author is grateful to Minsung Kim for providing some references.\r\nThe first author has been supported by the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101034413. The second author has been supported by the NSF grant DMS 2246983.","scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","month":"11","publisher":"Instituto Nacional de Matematica Pura e Aplicada","arxiv":1,"citation":{"ama":"CZUDEK KS, Dolgopyat D. The central limit theorem and rate of mixing for simple random walks on the circle. <i>Alea</i>. 2024;21(2):1853-1865. doi:<a href=\"https://doi.org/10.30757/ALEA.V21-70\">10.30757/ALEA.V21-70</a>","mla":"CZUDEK, Klaudiusz S., and Dmitry Dolgopyat. “The Central Limit Theorem and Rate of Mixing for Simple Random Walks on the Circle.” <i>Alea</i>, vol. 21, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2024, pp. 1853–65, doi:<a href=\"https://doi.org/10.30757/ALEA.V21-70\">10.30757/ALEA.V21-70</a>.","ista":"CZUDEK KS, Dolgopyat D. 2024. The central limit theorem and rate of mixing for simple random walks on the circle. Alea. 21(2), 1853–1865.","ieee":"K. S. CZUDEK and D. Dolgopyat, “The central limit theorem and rate of mixing for simple random walks on the circle,” <i>Alea</i>, vol. 21, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1853–1865, 2024.","chicago":"CZUDEK, Klaudiusz S, and Dmitry Dolgopyat. “The Central Limit Theorem and Rate of Mixing for Simple Random Walks on the Circle.” <i>Alea</i>. Instituto Nacional de Matematica Pura e Aplicada, 2024. <a href=\"https://doi.org/10.30757/ALEA.V21-70\">https://doi.org/10.30757/ALEA.V21-70</a>.","apa":"CZUDEK, K. S., &#38; Dolgopyat, D. (2024). The central limit theorem and rate of mixing for simple random walks on the circle. <i>Alea</i>. Instituto Nacional de Matematica Pura e Aplicada. <a href=\"https://doi.org/10.30757/ALEA.V21-70\">https://doi.org/10.30757/ALEA.V21-70</a>","short":"K.S. CZUDEK, D. Dolgopyat, Alea 21 (2024) 1853–1865."},"external_id":{"arxiv":["2404.11700"],"isi":["001440992000003"]},"date_updated":"2025-09-08T14:48:42Z","type":"journal_article","year":"2024","project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"publication":"Alea","publication_identifier":{"issn":["1980-0436"]},"date_published":"2024-11-01T00:00:00Z","author":[{"full_name":"Czudek, Klaudiusz S","last_name":"Czudek","id":"5c0e116e-803f-11ed-ab7e-90d572405f20","first_name":"Klaudiusz S"},{"full_name":"Dolgopyat, Dmitry","last_name":"Dolgopyat","first_name":"Dmitry"}],"volume":21,"intvolume":"        21"},{"article_type":"original","article_processing_charge":"No","page":"1311-1334","ec_funded":1,"issue":"2","status":"public","date_created":"2018-12-11T11:44:28Z","title":"Transition to shocks in TASEP and decoupling of last passage times","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"_id":"70","ddc":["510"],"day":"01","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"abstract":[{"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.","lang":"eng"}],"isi":1,"publication_status":"published","doi":"10.30757/ALEA.v15-49","author":[{"last_name":"Nejjar","full_name":"Nejjar, Peter","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2020-07-14T12:47:46Z","volume":15,"intvolume":"        15","date_published":"2018-10-01T00:00:00Z","file":[{"date_updated":"2020-07-14T12:47:46Z","content_type":"application/pdf","creator":"kschuh","checksum":"2ded46aa284a836a8cbb34133a64f1cb","relation":"main_file","file_size":394851,"file_name":"2018_ALEA_Nejjar.pdf","file_id":"5981","date_created":"2019-02-14T09:44:10Z","access_level":"open_access"}],"publication":"Latin American Journal of Probability and Mathematical Statistics","has_accepted_license":"1","publication_identifier":{"issn":["1980-0436"]},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"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>.","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>.","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.","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>","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334."},"date_updated":"2025-04-14T07:27:49Z","external_id":{"arxiv":["1705.08836"],"isi":["000460475800022"]},"type":"journal_article","year":"2018","publisher":"Instituto Nacional de Matematica Pura e Aplicada","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","month":"10","scopus_import":"1"}]