# Classification of Stationary distributions for the stochastic vertex models

@inproceedings{Lin2022ClassificationOS, title={Classification of Stationary distributions for the stochastic vertex models}, author={Yier Lin}, year={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 the S6V model are given by product Bernoulli measures. Moreover, for the S6V model under a moving frame with speed 1, we show that the extreme stationary distributions are given by product Bernoulli measures and blocking measures. In the end, we generalize our results to the stochastic higher spin…

## References

SHOWING 1-10 OF 79 REFERENCES

Six-vertex models and the GUE-corners process

- Mathematics
- 2016

In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models 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…

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

- Mathematics
- 2020

In this paper we consider the Higher Spin Six Vertex Model on the lattice
$${\mathbb {Z}}_{\ge 2} \times {\mathbb {Z}}_{\ge 1}$$
. We first identify a family of translation invariant measures and…

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…

Dynamical stochastic higher spin vertex models

- Mathematics
- 2017

We introduce a new family of integrable stochastic processes, called dynamical stochastic higher spin vertex models, arising from fused representations of Felder’s elliptic quantum group $$E_{\tau ,…

Stochastic Higher Spin Vertex Models on the Line

- Mathematics
- 2015

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain…

The stochastic telegraph equation limit of the stochastic higher spin six vertex model

- Mathematics
- 2020

In this paper, we prove that the stochastic telegraph equation arises as a scaling limit of the stochastic higher spin six vertex (SHS6V) model with general spin $I/2, J/2$. This extends results of…

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…

Current fluctuations of the stationary ASEP and six-vertex model

- Mathematics
- 2018

Our results in this paper are two-fold. First, we consider current fluctuations of the stationary asymmetric simple exclusion process (ASEP), run for some long time $T$, and show that they are of…