# Dynamical Stochastic Higher Spin Vertex Models

## TL;DR

This paper introduces a new class of integrable stochastic models called dynamical stochastic higher spin vertex models, which generalize previous models and exhibit unique asymptotic behavior in their current distributions.

## Contribution

The paper develops a new family of integrable stochastic processes based on elliptic quantum groups, extending prior models and providing explicit integral identities for their observables.

## Key findings

- Derived explicit contour integral identities for model observables.
- Analyzed asymptotic behavior of the current in a special case.
- Established the scaling exponent as 1/4 and characterized the limiting distribution.

## Abstract

We introduce a new family of integrable stochastic processes, called \textit{dynamical stochastic higher spin vertex models}, arising from fused representations of Felder's elliptic quantum group $E_{\tau, \eta} (\mathfrak{sl}_2)$. These models simultaneously generalize the stochastic higher spin vertex models, studied by Corwin-Petrov and Borodin-Petrov, and are dynamical in the sense of Borodin's recent stochastic interaction round-a-face models. We provide explicit contour integral identities for observables of these models (when run under specific types of initial data) that characterize the distributions of their currents. Through asymptotic analysis of these identities in a special case, we evaluate the scaling limit for the current of a dynamical version of a discrete-time partial exclusion process. In particular, we show that its scaling exponent is $1 / 4$ and that its one-point marginal converges (in a sense of moments) to that of a non-trivial random variable, which we determine explicitly.