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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Multipoint distribution of periodic TASEP
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by Jinho Baik and Zhipeng Liu HTML | PDF
J. Amer. Math. Soc. 32 (2019), 609-674 Request permission

Abstract:

The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process or its variations. However, the temporal process, or more generally the two-dimensional space-time fluctuation field, is less well understood. We consider this question for the periodic TASEP (totally asymmetric simple exclusion process). For a particular initial condition, we evaluate the multitime and multilocation distribution explicitly in terms of a multiple integral involving a Fredholm determinant. We then evaluate the large-time limit in the so-called relaxation time scale.
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Additional Information
  • Jinho Baik
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 646186
  • Email: baik@umich.edu
  • Zhipeng Liu
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
  • MR Author ID: 1054102
  • Email: zhipeng@ku.edu
  • Received by editor(s): October 18, 2017
  • Received by editor(s) in revised form: October 26, 2018
  • Published electronically: January 8, 2019
  • Additional Notes: The first author was supported in part by NSF grants DMS-1361782, DMS-1664531, and DMS-1664692, and the Simons Fellows program. The work was done in part when the second author was at Courant Institute, New York University.
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 32 (2019), 609-674
  • MSC (2010): Primary 60K35; Secondary 82C22
  • DOI: https://doi.org/10.1090/jams/915
  • MathSciNet review: 3981984