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 | References | Similar Articles | Additional Information
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
Email:
baik@umich.edu
Zhipeng Liu
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email:
zhipeng@ku.edu
DOI:
https://doi.org/10.1090/jams/915
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.
Article copyright:
© Copyright 2019
American Mathematical Society