---
OA_place: repository
OA_type: green
_id: '18586'
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."
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."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Klaudiusz S
  full_name: Czudek, Klaudiusz S
  id: 5c0e116e-803f-11ed-ab7e-90d572405f20
  last_name: Czudek
- first_name: Dmitry
  full_name: Dolgopyat, Dmitry
  last_name: Dolgopyat
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>
  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>
  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>.
  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.
  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.
  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>.
  short: K.S. CZUDEK, D. Dolgopyat, Alea 21 (2024) 1853–1865.
date_created: 2024-11-24T23:01:49Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T14:48:42Z
day: '01'
department:
- _id: VaKa
doi: 10.30757/ALEA.V21-70
ec_funded: 1
external_id:
  arxiv:
  - '2404.11700'
  isi:
  - '001440992000003'
intvolume: '        21'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2404.11700'
month: '11'
oa: 1
oa_version: Preprint
page: 1853-1865
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Alea
publication_identifier:
  issn:
  - 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: The central limit theorem and rate of mixing for simple random walks on the
  circle
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 21
year: '2024'
...
---
_id: '70'
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
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>
  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>
  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.
  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>.
  short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics
    15 (2018) 1311–1334.
date_created: 2018-12-11T11:44:28Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v15-49
ec_funded: 1
external_id:
  arxiv:
  - '1705.08836'
  isi:
  - '000460475800022'
file:
- access_level: open_access
  checksum: 2ded46aa284a836a8cbb34133a64f1cb
  content_type: application/pdf
  creator: kschuh
  date_created: 2019-02-14T09:44:10Z
  date_updated: 2020-07-14T12:47:46Z
  file_id: '5981'
  file_name: 2018_ALEA_Nejjar.pdf
  file_size: 394851
  relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: '        15'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1311-1334
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Latin American Journal of Probability and Mathematical Statistics
publication_identifier:
  issn:
  - 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transition to shocks in TASEP and decoupling of last passage times
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...