# Strong law of large numbers for the stochastic six vertex model

@inproceedings{Drillick2022StrongLO, title={Strong law of large numbers for the stochastic six vertex model}, author={Hindy Drillick and Yier Lin}, year={2022} }

. We consider the inhomogeneous stochastic six vertex model with periodicity starting from step initial data. We prove that it converges almost surely to a deterministic limit shape. For the proof, we map the stochastic six vertex model to a deformed version of the discrete Hammersley process [Sep97, BEGG16]. Then we construct a colored version of the model and apply Liggett’s superadditive ergodic theorem. The construction of the colored model includes a new idea using a Boolean-type product…

## References

SHOWING 1-10 OF 30 REFERENCES

### Classification of Stationary distributions for the stochastic vertex models

- Mathematics
- 2022

. In this paper, we study the stationary distribution for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extreme stationary distributions of…

### 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…

### 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…

### Stochastic PDE Limit of the Six Vertex Model

- MathematicsCommunications in Mathematical Physics
- 2020

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase…

### Stochastic telegraph equation limit for the stochastic six vertex model

- MathematicsProceedings of the American Mathematical Society
- 2019

In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin (2018), where the weights of corner-shape vertices are tuned to zero, and prove Conjecture 6.1…

### A short note on Markov duality in multi–species higher spin stochastic vertex models

- MathematicsElectronic Communications in Probability
- 2021

We show that the multi-species higher spin stochastic vertex model, also called the U_q(A_n^{(1)}) vertex model, satisfies a duality where the indicator function has the form {\eta^x_{[1,n]} \geq…

### Limit Shapes of the Stochastic Six Vertex Model

- MathematicsCommunications in Mathematical Physics
- 2018

It is shown that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these equations are…

### 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.

### Convergence of the Stochastic Six-Vertex Model to the ASEP

- Mathematics
- 2016

In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by…

### A stochastic telegraph equation from the six-vertex model

- MathematicsThe Annals of Probability
- 2019

A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are…