Observables of coloured stochastic vertex models and their polymer limits

Abstract

In the context of the coloured stochastic vertex model in a quadrant, we identify a family of observables whose averages are given by explicit contour integrals. The observables are certain linear combinations of $q$-moments of the coloured height functions of the model. In a polymer limit, this yields integral representations for moments of partition functions of strict-weak, semi-discrete Brownian, and continuum Brownian polymers with varying beginning and ending points of the polymers.