Observables of stochastic colored vertex models and local relation

TL;DR

This paper derives integral formulas for joint q-moments of height functions in the stochastic colored six vertex model, introducing a new local relation that enhances understanding of the model's observables and symmetries.

Contribution

It provides the first integral expression for observables of the SC6V model and introduces a novel local relation of height functions, generalizing previous results.

Findings

Integral expression for joint q-moments of height functions

New local relation of height functions in neighboring points

Alternative proof of symmetry properties of SC6V height functions

Abstract

We study the stochastic colored six vertex (SC6V) model and its fusion. Our main result is an integral expression for natural observables of this model -- joint q-moments of height functions. This generalises a recent result of Borodin-Wheeler. The key technical ingredient is a new relation of height functions of SC6V model in neighboring points. This relation is of independent interest; we refer to it as a local relation. As applications, we give a new proof of certain symmetries of height functions of SC6V model recently established by Borodin-Gorin-Wheeler and Galashin, and new formulas for joint moments of delayed partition functions of Beta polymer.