Classification of Stationary distributions for the stochastic vertex models

Yier Lin

Classification of Stationary distributions for the stochastic vertex models

Probability 2023-03-23 v2

Authors: Yier Lin

Abstract

In this paper, we study the stationary distributions for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extremal stationary distributions of the S6V model are given by product Bernoulli measures. Moreover, for the S6V model under a moving frame of speed $1$ , we show that the extremal stationary distributions are given by product Bernoulli measures and blocking measures. Finally, we generalize our results to the stochastic higher spin six vertex model. Our proof relies on the coupling of the S6V models introduced in [Aggarwal, 2020], the analysis of current and the method of fusion.

Keywords

stochastic vertex model stationary distribution six vertex model bernoulli measure blocking measure coupling fusion

Cite

@article{arxiv.2205.10654,
  title  = {Classification of Stationary distributions for the stochastic vertex models},
  author = {Yier Lin},
  journal= {arXiv preprint arXiv:2205.10654},
  year   = {2023}
}

Comments

31 pages, 12 figures. Updated to improve the presentation of the paper and to correct some typos and errors. Some proofs are provided with more detail

Classification of Stationary distributions for the stochastic vertex models

Abstract

Keywords

Cite

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