Multi-point distribution of periodic TASEP
arXiv:1710.03284
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.
arXiv comment59 pages,7 figures, corrected some typos, modified Remarks 2.4 and 2.6
References in corpus (16)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Discrete polynuclear growth and determinantal processes
- Exact Large Deviation Function in the Asymmetric Exclusion Process
- Asymptotics in ASEP with Step Initial Condition
- Fluctuation properties of the TASEP with periodic initial configuration
- Exact Solution of the Master Equation for the Asymmetric Exclusion Process
- The KPZ fixed point
- Fluctuations of the one-dimensional polynuclear growth model with external sources
- Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
- Exact Non-Stationary Probabilities in the Asymmetric Exclusion Process on a Ring
- Finite-time fluctuations for the totally asymmetric exclusion process
- Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
- On Time Correlations for KPZ Growth in One Dimension
- Two-time free energy distribution function in (1+1) directed polymers
- On two-time distribution functions in (1+1) random directed polymers
- Determinant solution for the TASEP with particle-dependent hopping probabilities on a ring