Multipoint distribution of periodic TASEP

Baik, Jinho; Liu, Zhipeng

doi:10.1090/jams/915

Multipoint distribution of periodic TASEP

Authors: Jinho Baik and Zhipeng Liu
Journal: J. Amer. Math. Soc. 32 (2019), 609-674
MSC (2010): Primary 60K35; Secondary 82C22
DOI: https://doi.org/10.1090/jams/915
Published electronically: January 8, 2019
MathSciNet review: 3981984
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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.

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