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.…
Long and Short Time Asymptotics of the Two-Time Distribution in Local Random Growth
- 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…
References
SHOWING 1-10 OF 43 REFERENCES
Fluctuations in the Discrete TASEP with Periodic Initial Configurations and the Airy1 Process
- Mathematics
- 2006
We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with sequential update. The joint distribution of the positions of selected particles is expressed as a Fredholm…
Transition between Airy1 and Airy2 processes and TASEP fluctuations
- Computer Science
- 2007
In this paper the totally asymmetric simple exclusion process is considered, a model in the KPZ universality class, and its one‐point distribution is a new interpolation between GOE and GUE edge distributions.
Fluctuation Properties of the TASEP with Periodic Initial Configuration
- Mathematics
- 2007
Abstract
We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a…
Fluctuations of TASEP on a Ring in Relaxation Time Scale
- Mathematics
- 2016
We consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions. We assume that the size of the ring and the number of particles tend to infinity…
Limit process of stationary TASEP near the characteristic line
- Mathematics
- 2010
The totally asymmetric simple exclusion process (TASEP) on\input amssym ${\Bbb Z}$ with the Bernoulli‐ρ measure as an initial condition, 0 < ρ < 1, is stationary. It is known that along the…
Limit Processes for TASEP with Shocks and Rarefaction Fans
- Mathematics
- 2010
We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density ρ− and right density ρ+. We study the associated height…
Height fluctuations of stationary TASEP on a ring in relaxation time scale
- Physics
- 2016
We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional…
Fluctuations of TASEP and LPP with general initial data
- Mathematics
- 2014
We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a…
Large time asymptotics of growth models on space-like paths I: PushASEP
- Mathematics
- 2007
We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied,…
21pYO-3 Spatial correlations of the 1D KPZ surface on a flat substrate
- Mathematics
- 2005
We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm…