Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

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

 
 

 

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
Full-text PDF
View in AMS MathViewer New

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 60K35, 82C22

Retrieve articles in all journals with MSC (2010): 60K35, 82C22


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