Higher spin six vertex model and symmetric rational functions

TL;DR

This paper develops integral formulas for multi-point q-moments and q-correlation functions in an inhomogeneous higher spin six vertex model, connecting it to known integrable probabilistic systems within the KPZ universality class.

Contribution

It introduces symmetric rational functions as partition functions for the model and derives Cauchy-like identities from the Yang-Baxter equation, extending previous work on related polynomials.

Findings

Derived integral representations for multi-point q-moments and q-correlation functions.

Established connections to known models like ASEP and q-TASEP in certain limits.

Proved Cauchy-like identities for symmetric rational functions from Yang-Baxter equation.

Abstract

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the q-correlation functions. At least in the case of the step initial condition, our formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six vertex model, ASEP, various q-TASEPs, and associated zero range processes. Our arguments are largely based on properties of a family of symmetric rational functions which can be defined as partition functions of the inhomogeneous higher spin six vertex model for suitable domains. In the homogeneous case, such functions were previously studied in http://arxiv.org/abs/1410.0976; they also generalize classical Hall-Littlewood and Schur polynomials. A key role is played by Cauchy-like summation identities for these functions, which are obtained as a direct corollary of the Yang-Baxter equation for the higher spin six vertex model.