Classification of Stationary distributions for the stochastic vertex models

Yier Lin

Published 2022-05-21Version 1

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 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.