  Vertical-arrow fluctuations near the boundaries in the six-vertex model on
the two-dimensional $N \times N$ square lattice with the domain wall boundary
conditions are considered. The one-point correlation function (`boundary
polarization') is expressed via the partition function of the model on a
sublattice. The partition function is represented in terms of standard objects
in the theory of orthogonal polynomials. This representation is used to study
the large N limit: the presence of the boundary affects the macroscopic
quantities of the model even in this limit. The logarithmic terms obtained are
compared with predictions from conformal field theory.
