Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model

The five-vertex model on a square lattice with fixed boundary conditions, which corresponds to the weighted (with the weight $q$ per elementary cube) enumerations of boxed plane partition is considered. The one-point correlation function of the model describing the probability of a given state on an edge (polarization) is calculated. This generalises the similar result obtained previously by the authors for the unweighed (weighted with the weight $q=1$) enumerations of plane partitions.