# Color-position symmetry in interacting particle systems

@article{Borodin2019ColorpositionSI, title={Color-position symmetry in interacting particle systems}, author={Alexei Borodin and Alexey Bufetov}, journal={The Annals of Probability}, year={2019} }

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir-Angel-Valko and Borodin-Wheeler. We are also able to use the symmetry, together with previously known results for uncolored…

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## References

SHOWING 1-10 OF 60 REFERENCES

Stochastic six-vertex model

- Mathematics
- 2016

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit…

From interacting particle systems to random matrices

- Mathematics
- 2010

In this contribution we consider stochastic growth models in the Kardar–Parisi–Zhang universality class in 1 + 1 dimension. We discuss the large time distribution and processes and their dependence…

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,…

Shock fluctuations in asymmetric simple exclusion

- Mathematics
- 1992

SummaryThe one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the…

Busemann functions and the speed of a second class particle in the rarefaction fan

- Mathematics
- 2010

In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89–125], about the Busemann functions in last-passage percolation, can be used to calculate the…

Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model

- MathematicsCommunications in Mathematical Physics
- 2019

In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is…

Hydrodynamic equations for attractive particle systems on ℤ

- Mathematics
- 1987

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as…

Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian.

- PhysicsPhysical review letters
- 1992

It is proved that the dynamical scaling exponent for kinetic roughening is z=3/2 in 1+1 dimensions and diagonalize it using the Bethe ansatz and predict the large-scale asymptotic behavior of the vertical polarization correlations.

Shock profiles for the asymmetric simple exclusion process in one dimension

- Mathematics
- 1997

AbstractThe asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left…

The TASEP speed process.

- Mathematics
- 2011

In the multi-type totally asymmetric simple exclusion process (TASEP), each site ofZ is occupied by a labeled particle, and two neighboring particles are int erchanged at rate one if their labels are…