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

We consider the five-vertex model on a square lattice with fixed boundary conditions which corresponds to weighted (with weight q per elementary cube) enumerations of boxed plane partitions. We calculate the one-point correlation function of the model which describes the probability of a given state on an edge (polarization). This generalizes an analogous result obtained previously by the authors for unweighted (weighted with weight q = 1) enumerations of plane partitions. Bibliography: 14 titles.