# Multipoint distribution of periodic TASEP

@article{Baik2019MultipointDO, title={Multipoint distribution of periodic TASEP}, author={Jinho Baik and Zhipeng Liu}, journal={Journal of the American Mathematical Society}, year={2019} }

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…

## 44 Citations

Limiting one-point distribution of periodic TASEP

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in…

Periodic TASEP with general initial conditions

- MathematicsProbability Theory and Related Fields
- 2020

We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point…

Multi-point distribution of discrete time periodic TASEP

- MathematicsProbability Theory and Related Fields
- 2022

We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula…

Nonstationary Generalized TASEP in KPZ and Jamming Regimes

- PhysicsJournal of Statistical Physics
- 2021

We study the model of the totally asymmetric exclusion process with generalized update, which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing…

From the Riemann surface of TASEP to ASEP

- Mathematics
- 2021

We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward hopping rate q and periodic boundary conditions. We show that the Bethe equations of ASEP can be…

KP governs random growth off a 1-dimensional substrate

- Mathematics, PhysicsForum of Mathematics, Pi
- 2022

Abstract The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation.…

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- Mathematics
- 2019

The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in…

Time-time Covariance for Last Passage Percolation with Generic Initial Profile

- MathematicsMathematical Physics, Analysis and Geometry
- 2019

We consider time correlation for KPZ growth in 1 + 1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In…

Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume

- MathematicsJournal of Statistical Physics
- 2018

Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium…

Time evolution of the Kardar-Parisi-Zhang equation

- Mathematics
- 2020

The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The…

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Abstract
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