Multi-point distribution of periodic TASEP

2017/10/09 by Jinho Baik, Zhipeng Liu, Baik, Jinho +1 · 10 citations
Mathematics · Physics and Astronomy · #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 #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1710.03284

59 pages,7 figures, corrected some typos, modified Remarks 2.4 and 2.6

openalex publication_date 2017/10/09 · arxiv created 2018/10/26 · arxiv updated 2018/10/30 · 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
• Scaling Properties of Current Fluctuations in Periodic TASEP
• Dynamic scaling of growing interfaces
• The half-space Airy stat process
• Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring
• Revisiting the temporal law in KPZ random growth
• Bethe roots for periodic TASEP and algebraic curve
• Reduced Random Walks in the Hyperbolic Plane\hspace1pt!\hspace-3.8pt?
• Large time cumulants of the KPZ equation on an interval
• Riemann surfaces for KPZ with periodic boundaries
• Time-time Covariance for Last Passage Percolation with Generic Initial Profile

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• Periodic KPZ fixed point with general initial conditions
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