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 [4], the analysis of current and the method of fusion.
Acknowledgments
The author thanks Amol Aggarwal, Ivan Corwin and Pablo Ferrari for helpful discussion. We also thank Amol Aggarwal and Ivan Corwin for helpful comments on the paper. We are grateful to three anonymous referees, who provide plenty of useful suggestions which improve the presentation of the paper significantly. This paper is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while the author participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2021 semester.
Citation
Yier Lin. "Classification of stationary distributions for the stochastic vertex models." Electron. J. Probab. 28 1 - 40, 2023. https://doi.org/10.1214/23-EJP1022
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