## Multipoint distribution of periodic TASEP

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Jinho Baik and Zhipeng Liu
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## 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.## References

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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