Multi-point distribution of periodic TASEP

2017/10/09 by Jinho Baik, Zhipeng Liu, Baik, Jinho +1 · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1710.03284

openalex publication_date 2017/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 multi-time and multi-location 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.

Citations

• Fluctuations of the one-dimensional polynuclear growth model with external sources
• The KPZ fixed point

Cited by

• Multipoint distributions of the KPZ fixed point with compactly supported initial conditions

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• Periodic TASEP with general initial conditions
• Multi-point distribution of discrete time periodic TASEP
• Limiting one-point distribution of periodic TASEP
• Periodic KPZ fixed point with general initial conditions
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