• Corpus ID: 254877062

Strong law of large numbers for the stochastic six vertex model

  title={Strong law of large numbers for the stochastic six vertex model},
  author={Hindy Drillick and Yier Lin},
. 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… 



Classification of Stationary distributions for the stochastic vertex models

. 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

  • A. Aggarwal
  • Mathematics
    Communications 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

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

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

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

  • Jeffrey Kuan
  • Mathematics
    Electronic 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

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.

  • GwaSpohn
  • Physics
    Physical 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

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

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