Multipoint distribution of periodic TASEP

Baik, Jinho¹ ; Liu, Zhipeng²

¹Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
²Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

Journal of the American Mathematical Society, Tome 32 (2019) no. 3, pp. 609-674

Résumé

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.

Détail

DOI : 10.1090/jams/915

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