# Yang-Baxter random fields and stochastic vertex models

## TL;DR

This paper introduces new Yang-Baxter random fields of Young diagrams using bijectivization, connecting them to stochastic vertex models and deriving explicit formulas for their height function distributions.

## Contribution

It develops novel Yang-Baxter random fields based on spin $q$-Whittaker and spin Hall-Littlewood functions, linking them to key stochastic vertex models and providing explicit distribution formulas.

## Key findings

- Matched scalar marginals with stochastic six vertex models
- Derived Fredholm determinantal formulas for height functions
- Discovered diagonal difference operators for symmetric functions

## Abstract

Bijectivization refines the Yang-Baxter equation into a pair of local Markov moves which randomly update the configuration of the vertex model. Employing this approach, we introduce new Yang-Baxter random fields of Young diagrams based on spin $q$-Whittaker and spin Hall-Littlewood symmetric functions. We match certain scalar Markovian marginals of these fields with (1) the stochastic six vertex model; (2) the stochastic higher spin six vertex model; and (3) a new vertex model with pushing which generalizes the $q$-Hahn PushTASEP introduced recently by Corwin-Matveev-Petrov (arXiv:1811.06475). Our matchings include models with two-sided stationary initial data, and we obtain Fredholm determinantal expressions for the $q$-Laplace transforms of the height functions of all these models. Moreover, we also discover difference operators acting diagonally on spin $q$-Whittaker or (stable) spin Hall-Littlewood symmetric functions.